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We consider a (non) zero-sum differential game between two insurers and determine a robust reinsurance contract from joint interests of the insurers and the reinsurer under the framework of Stackelberg differential game, that is, a hybrid stochastic differential game framework is introduced in this article. We assume that each party can invest in a financial market consisting of a risk-free asset and a risky asset whose price evolution follows a stochastic volatility model, and the reinsurer charges the premium according to both the expected value premium principle and the variance premium principle. Since the performance-related capital inflow or outflow feature is introduced, the insurers and reinsurer all aim to maximize their own time-inconsistent mean-variance criterion with delay. Using the dynamic programming approach, we derive the equilibrium investment strategy, the robust equilibrium reinsurance contract, and the corresponding equilibrium value functions under two premium principles with certain conditions, respectively. Some interesting properties of the equilibrium investment strategy are proved explicitly, and several numerical examples and sensitivity analysis are presented to demonstrate the effects of model parameters on the equilibrium reinsurance contract. [ABSTRACT FROM AUTHOR]

This paper investigates the optimal investment-reinsurance problems for an ambiguity averse insurer with access to the options market, who worries about ambiguity and aims to find robust strategies to minimize the probability of ruin. The insurer is allowed to invest in the financial market, which consists of a risk-free asset and a risky asset, and purchase an option on another risky asset to hedge its risk. In addition, the insurer can purchase proportional reinsurance to transfer part of its claim risk. By applying dynamic programming principle, we obtain closed-form solutions for the corresponding optimal investment-reinsurance strategies and the value functions. We elucidate how investment options improve the insurer’s portfolio performance and find that the change in the correlation coefficient between the financial market and the options market can significantly affect the insurer’s optimal investment-reinsurance strategy. We also compare the effects of different ambiguity aversion coefficients in the markets and provide some numerical examples and economic explanations to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper discusses a robust Stackelberg differential investment and proportional reinsurance game for a reinsurance company and an insurance company, where the insurance company is treated as the follower and the reinsurance company is treated as the leader. The reinsurance company can set reinsurance premium price and invest its wealth in a savings account and a stock, where the price dynamic of the stock is governed by a jump-diffusion model. The insurance company can buy proportional reinsurance from the reinsurance company and trade in the same stock and savings account. Beside, we take historical performance into account. Both the reinsurance company and the insurance company are supposed to be ambiguity-averse and their purposes are to maximise the expected exponential utility of their final wealth with delay, respectively. By adopting stochastic control theory, we obtain the optimal value functions and robust equilibrium strategies explicitly. We also establish the corresponding verification theorem. Finally, we present numerical examples that demonstrate how the ambiguity aversion coefficients and other parameters affect the robust equilibrium strategies. [ABSTRACT FROM AUTHOR]

Loss reserving generally focuses on identifying a single model that can generate superior predictive performance. However, different loss reserving models specialise in capturing different aspects of loss data. This is recognised in practice in the sense that results from different models are often considered, and sometimes combined. For instance, actuaries may take a weighted average of the prediction outcomes from various loss reserving models, often based on subjective assessments. In this paper, we propose a systematic framework to objectively combine (i.e. ensemble) multiple stochastic loss reserving models such that the strengths offered by different models can be utilised effectively. Our framework contains two main innovations compared to existing literature and practice. Firstly, our criteria model combination considers the full distributional properties of the ensemble and not just the central estimate – which is of particular importance in the reserving context. Secondly, our framework is that it is tailored for the features inherent to reserving data. These include, for instance, accident, development, calendar, and claim maturity effects. Crucially, the relative importance and scarcity of data across accident periods renders the problem distinct from the traditional ensembling techniques in statistical learning. Our framework is illustrated with a complex synthetic dataset. In the results, the optimised ensemble outperforms both (i) traditional model selection strategies, and (ii) an equally weighted ensemble. In particular, the improvement occurs not only with central estimates but also relevant quantiles, such as the 75th percentile of reserves (typically of interest to both insurers and regulators). The framework developed in this paper can be implemented thanks to an R package, ADLP, which is available from CRAN. [ABSTRACT FROM AUTHOR]

Dybvig (1988a, 1988b) solves in a complete market setting the problem of finding a payoff that is cheapest possible in reaching a given target distribution ("cost-efficient payoff"). In the presence of ambiguity, the distribution of a payoff is, however, no longer known with certainty. We study the problem of finding the cheapest possible payoff whose worst-case distribution stochastically dominates a given target distribution ("robust cost-efficient payoff") and determine solutions under certain conditions. We study the link between "robust cost-efficiency" and the maxmin expected utility setting of Gilboa and Schmeidler (1989), as well as more generally in a possibly nonexpected robust utility setting. Specifically, we show that solutions to maxmin robust expected utility are necessarily robust cost-efficient. We illustrate our study with examples involving uncertainty both on the drift and on the volatility of the risky asset. [ABSTRACT FROM AUTHOR]

The theory of linear recurrence sequences is applied to obtain an explicit formula for the ultimate ruin probability in a discrete-time risk process. It is assumed that the claims distribution is arbitrary but has finite support { 0 , 1 , … , m + 1 } , for some integer m ≥ 1 . The method requires finding the zeroes of an m degree polynomial and solving a system of m linear equations. An approximation is derived and some numerical results and plots are provided as examples. [ABSTRACT FROM AUTHOR]

This paper derives several mathematical properties of the generalized Cramér–Lundberg model proposed by Tomita et al. (J. Appl. Probab. 59(3):849-859, 2022). The model extends the Bayesian-estimator model of Dubey. (Versicherungsmathematiker. 2:130-141, 1977) to the case of multiple insurance policies. We study the instantaneous premium function and the dependence structure of the ruin probability on the intensity of the driving mixed Poisson process. In particular, we show that the conditional ruin probability is monotonic with respect to the intensity value under certain assumptions. Monte Carlo simulations suggest that, without these assumptions, the monotonicity does not generally hold. Our study contributes to the risk management of insurance companies in the sense that it reveals how the difference between the assumed and true distribution of the risk factor affects the ruin probability. [ABSTRACT FROM AUTHOR]

We consider a continuous-time two-dimensional risk model, in which the claims from the two lines of insurance businesses satisfy an extensive asymptotic independence structure and the stochastic return is driven by a geometric Lévy process. Under a mild technical condition regarding the Laplace exponent of the Lévy process, we obtain explicit asymptotic expansions for both finite-time and infinite-time ruin probabilities when the claim sizes have regularly varying distributions. [ABSTRACT FROM AUTHOR]

In this article, we study dynamic risk measures by means of backward doubly stochastic Volterra integral equations (BDSVIEs, for short) with jumps. We establish the well-posedness of BDSVIEs with jumps in the sense of M-solution and prove a comparison theorem of BDSVIEs with jumps. Finally, we study properties of dynamic risk measures induced by BDSVIEs with jumps. Our results extend the well-posedness and the comparison theorem of BDSVIEs without jumps to the setting with jumps, and extend dynamic risk measures induced by BSDEs, BDSDEs, and BSVIEs to the case of BDSVIEs with jumps. [ABSTRACT FROM AUTHOR]

In this article, we consider the mixed ratcheting-periodic dividend strategies for spectrally negative Lévy risk model, in which dividend payments can both be made continuously without falling and discretely at the jump times of an independent Poisson process. The expected net present value of dividends paid up to ruin and the Laplace transform of the ruin time are obtained by using Lévy fluctuation theory. All the results are expressed in terms of scale functions. Finally, numerical results for Brownian motion with drift are given. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk. Since Mean Residual Life (MRL) has a close relationship with the tail of the distribution, we consider two classes of risk distributions, Decreasing Mean Residual Life (DMRL) and Increasing Mean Residual Life (IMRL) distributions, which can be used to classify light-tailed and heavy-tailed distributions, respectively. We assume that the underlying risk process is modelled by the classical Cramér-Lundberg model process. Under the mean-variance criterion, by solving the extended Hamilton-Jacobi-Bellman equation, we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL, respectively. Furthermore, we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance strategy. We find that under the case of DMRL, if the distribution and the risk aversions satisfy certain conditions, the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy, and under the case of IMRL, the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance. [ABSTRACT FROM AUTHOR]

A Systemic Optimal Risk Transfer Equilibrium (SORTE) was introduced in: "Systemic optimal risk transfer equilibrium", Mathematics and Financial Economics (2021), for the analysis of the equilibrium among financial institutions or in insurance-reinsurance markets. A SORTE conjugates the classical Bühlmann's notion of a risk exchange equilibrium with a capital allocation principle based on systemic expected utility optimization. In this paper we extend such a notion to the case when the value function to be optimized is multivariate in a general sense, and it is not simply given by the sum of univariate utility functions. This takes into account the fact that preferences of single agents might depend on the actions of other participants in the game. Technically, the extension of SORTE to the new setup requires developing a theory for multivariate utility functions and selecting at the same time a suitable framework for the duality theory. Conceptually, this more general framework allows us to introduce and study a Nash Equilibrium property of the optimizer. We prove existence, uniqueness, and the Nash Equilibrium property of the newly defined Multivariate Systemic Optimal Risk Transfer Equilibrium. [ABSTRACT FROM AUTHOR]

We establish a recursive representation that fully decouples jumps from a large class of multivariate inhomogeneous stochastic differential equations with jumps of general time-state dependent unbounded intensity, not of Lévy-driven type that essentially benefits a lot from independent and stationary increments. The recursive representation, along with a few related ones, are derived by making use of a jump time of the underlying dynamics as an information relay point in passing the past on to a previous iteration step to fill in the missing information on the unobserved trajectory ahead. We prove that the proposed recursive representations are convergent exponentially fast in the limit, and can be represented in a similar form to Picard iterates under the probability measure with its jump component suppressed. On the basis of each iterate, we construct upper and lower bounding functions that are also convergent towards the true solution as the iterations proceed. We provide numerical results to justify our theoretical findings. [ABSTRACT FROM AUTHOR]

This paper is devoted to asymptotic analysis for a continuous-time risk model with the insurance surplus process and the log-price process of the investment driven by two dependent jump-diffusion processes. We take into account arbitrary dependence between the insurance claims and their corresponding investment return jumps caused by a sequence of systematic factors, whose arrival times constitute a renewal counting process. Under the framework of regular variation, we obtain a simple and unified asymptotic formula for the finite-time ruin probability as the initial wealth becomes large. It turns out that, in the weakly dependent case, the tails of the claims determine the exact decay rate of the finite-time ruin probability while the investment return jumps only contribute to the coefficient of the asymptotic formula; however, in the strongly dependent case, they both produce essential impacts on the finite-time ruin probability which is under-estimated in the weakly dependent case. [ABSTRACT FROM AUTHOR]

We consider the optimal risk transfer from an insurance company to a reinsurer. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some crucial distinctions. In particular, the insurance company's surplus is here (as is routinely the case) approximated by a Brownian motion, as opposed to the geometric Brownian motion used to model assets in finance. Furthermore, risk exposure is dialled 'down' via reinsurance, rather than 'up' via risky investments. This leads to interesting qualitative differences in the optimal designs. In this paper, using the martingale method, we derive the optimal design as a function of proportional, non-cheap reinsurance design that maximises the quadratic utility of the terminal value of the insurance surplus. We also consider several realistic constraints on the terminal value: a strict lower boundary, the probability (Value at Risk) constraint, and the expected shortfall (conditional Value at Risk) constraints under the $ \mathbb {P} $ P and $ \mathbb {Q} $ Q measures, respectively. In all cases, the optimal reinsurance designs boil down to a combination of proportional protection and option-like protection (stop-loss) of the residual proportion with various deductibles. Proportions and deductibles are set such that the initial capital is fully allocated. Comparison of the optimal designs with the optimal portfolios in finance is particularly interesting. Results are illustrated. [ABSTRACT FROM AUTHOR]

We investigate an optimal reinsurance problem when the loss process exhibits jump clustering features and the insurance company has restricted information about the loss process. We maximise expected exponential utility of terminal wealth and show that an optimal strategy exists. By exploiting both the Kushner–Stratonovich and Zakai approaches, we provide the equation governing the dynamics of the (infinite-dimensional) filter and characterise the solution of the stochastic optimisation problem in terms of a BSDE, for which we prove existence and uniqueness of a solution. After discussing the optimal strategy for a general reinsurance premium, we provide more explicit results in some relevant cases. [ABSTRACT FROM AUTHOR]

Consider a renewal risk model with stochastic return and stochastic perturbation, where the price process of the investment portfolio is a geometric Lévy process. When the claim sizes have a dependence structure, we derive the asymptotics of the finite-time ruin probability for all subexponential claim sizes. Particularly, when the claim sizes come from a subclass of the subexponential distribution class, the finite-time ruin probability has been estimated for claim sizes with a general dependence structure. [ABSTRACT FROM AUTHOR]

This paper investigates a Stackelberg game between an insurer and a reinsurer under the α-maxmin mean-variance criterion. The insurer can purchase per-loss reinsurance from the reinsurer. With the insurer's feedback reinsurance strategy, the reinsurer optimizes the reinsurance premium in the Stackelberg game. The financial market consists of cash and stock with Heston's stochastic volatility. Both the insurer and reinsurer maximize their respective α-maxmin mean-variance preferences in the market. The criterion is time-inconsistent and we derive the equilibrium strategies by the extended Hamilton-Jacobi-Bellman equations. Similar to the non-robust case in [Li, D. & Young, V. R. (2022). Stackelberg differential game for reinsurance: mean-variance framework and random horizon. Insurance: Mathematics and Economics102, 42–55.], excess-of-loss reinsurance is the optimal form of reinsurance strategy for the insurer. The equilibrium investment strategy is determined by a system of Riccati differential equations. Besides, the equations determining the equilibrium reinsurance strategy and reinsurance premium rate are given semi-explicitly, which is simplified to an algebraic equation in a specific example. Numerical examples illustrate that the game between the insurer and reinsurer makes the insurance more radical when the agents become more ambiguity averse or risk averse. Furthermore, the level of ambiguity, ambiguity attitude, and risk attitude of the insurer (reinsurer) have similar effects on the equilibrium reinsurance strategy, reinsurance premium, and investment strategy. [ABSTRACT FROM AUTHOR]

During extreme events such as natural or man-made disasters, it is likely that after immediate claims directly caused by the events, there are other delayed claims occurring in a certain period of future. In the classical risk model, each immediate claim is accompanied with a delayed one, but in reality each immediate claim can lead to a random number of delayed ones. To this end, we consider an insurance risk model with a random number of delayed claims as well as Brownian perturbation, dependence structures and constant interest force, and explore asymptotic estimations for an insurer's ruin-related risks exposed to the extreme events. This article provides a novel insight to model and analyze the potential risks by fully considering the ongoing impacts of heavy-tailed claims, and thus accurately assesses the insurer's operation risk in the long run. [ABSTRACT FROM AUTHOR]

The intensity, hardness, and extent of catastrophic accidents in recent decades have led insurance companies to seek resources to raise the capital to deal with the caused damage by these accidents. One of the most effective tools to cover the risk of catastrophic events such as earthquakes, floods, etc., which is widely used in the world, is catastrophic bonds. The purpose of this study is to provide a model for the pricing of catastrophic bonds. Because earthquake catastrophic damage causes major changes to corporate assets as well as investment trends, a jump sentence is added to the study model to indicate the severity and probability of damage. To produce the time discretization, the suggested methodology employs a one-order correct expression in the first process. To generate the full-discretization in the second level, the spectral collocation method approach that relies on the Chebyshev basis of the second kind is presented. Adding the jump sentence causes the original model to become an integral differential model, which approximates using the spectral method. Also, based on the derivatives in the obtained model, we approximated the derivative operator by using this type of base. The numerical investigation confirms the temporal discretized formulation's stability and convergence. We also approximated the integral sentence using the expansion of Gauss-Laguerre quadrature and presented numerical results. [ABSTRACT FROM AUTHOR]

In this paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied by the expected discounted dividend payments and the Gerber-Shiu function are derived. Then, the approximate solutions of the integro-differential equations are obtained through the sinc method. Finally, the numerical examples are given when the claim sizes follow different distributions. Furthermore, the errors between the explicit solution and the numerical solution are discussed in a special case. [ABSTRACT FROM AUTHOR]

The central mathematical tool discussed is a non-standard family of polynomials, univariate and bivariate, called Abel-Goncharoff polynomials. First, we briefly summarize the main properties of this family of polynomials obtained in the previous work. Then, we extend the remarkable links existing between these polynomials and the parking functions which are a classic object in combinatorics and computer science. Finally, we use the polynomials to determine the non-ruin probabilities over a finite horizon for a bivariate risk process, in discrete and continuous time, assuming that claim amounts are dependent via a partial Schur-constancy property.

To reduce investment risk in financial markets, how to select effective factors and determine factor weights to construct an effective portfolio is the focus of current research. In this paper, we build a multi-factor quantitative model and explore the long-term equilibrium relationship and short-term volatility impact relationship of investment risk in financial markets with the help of econometric models and the impulse response analysis of the dynamic correlation of risk. Johansen cointegration test and error correction model are used for the analysis to examine the long-term equilibrium relationship and short-term volatility impact of financial market risk. Secondly, the correlations and influencing factors among the risks in each market under the financial market are explored by simple correlation coefficient analysis and the Granger causality test. Finally, the dynamic correlation of risk is examined by impulse response analysis. The results of the study show that the accuracy of similarity-weighted voting portfolio forecasts are all the highest, and their accuracy rates are 93.2%, 95.7%, and 96.8% in years (t-1) to (t-3), which are above 90%, respectively. The method in this paper can better detect the risky situations that are likely to occur in the next three years for financial market investments and identify them with superior results.

With the development of socialist market economy, enterprises are faced with an increasingly complex development environment. In the context of socialist market economy, enterprises can only obtain better development if they continuously promote the improvement of internal control and management system, and effectively carry out financial risk control and management. This paper discusses the procedures and construction measures of the internal control and management system of the enterprise from the requirements and contents of the enterprise financial risk management, using the F-score model. We hope to strengthen the exploration of enterprise financial risk management measures by further improving the enterprise’s internal control system, so as to further enhance the quality of enterprise financial risk management, effectively predict, prevent, control and respond to the relevant financial risks of the enterprise, and build a stable development path for the enterprise.

The international capital flows between the financial markets of state-owned enterprises are frequent and closely linked, and the difficulty of assessing and managing risks is deepening day by day. In order to be able to provide some useful references for corporate financial institutions in theory and practice, this paper is oriented to cloud accounting SOEs, modeling and calculating SOE returns and volatilities to obtain corporate financial spillover indices. The calculated spillover index is introduced into the basic assessment system to establish the financial risk assessment system. Based on the expert scoring results of the assessment indexes, a judgment matrix is constructed to obtain the fuzzy assessment weights of each index. Combined with the system assessment results, the risk matrix is used to classify risk levels and develop corresponding management strategies. It is experimentally verified that the intensity of the total risk spillover index and the probability of risk occurrence between different submarkets of corporate finance are higher during the unpracticed period, 76% and 83.48%, respectively. In contrast, the spillover index intensity and the probability of risk occurrence in the practice period are only 50% and 61.15%. This shows that the proposed method can carry out effective risk assessment management based on the spillover index, which meets the needs of the times and realistic needs of cloud accounting SOEs for financial risk assessment management and promotes the financial business development of SOEs.

Relying on their low-cost comparative advantage, Chinese enterprises have rapidly integrated into the global industrial division of the labor system, entering the fast lane of development and becoming an important driving force behind China’s rapid economic growth. Furthermore, in recent years, this situation is changing. The cost of financing for Chinese companies has been rising yearly, a trend that has become increasingly evident, especially after the new crown epidemic. Investment growth in China’s capital markets has declined, the market has seen back-to-back years of decline, and competition has become more intense. It is imperative that enterprises need to strengthen their financial cost control management to enhance their competitiveness in the market by improving cost management. Cloud computing is a new model that relies on the Internet, with a certain amount of network storage space, scalability, and fast scaling. The development of cloud computing provides new ideas for target BPO cost management. With cloud computing, target BPO cost management becomes easier, making it a market-oriented cost control strategy for enterprises, especially those in a competitive market environment. Target BPO cost management can cover the whole process from financing to revenue through the decomposition and control of cost control objectives in various aspects. The ultimate effect is to improve the cost management level and enhance enterprise management’s efficiency. Based on the theories related to target BPO cost management at home and abroad, this paper takes 6201 listed companies in China as the object of research on cost control. The three hypotheses that financial BPO cost mitigates the company’s financial risk, financial BPO control reduces the company’s financial cost and improves the revenue of listed companies are verified by establishing a financial cost mediation effect model through nine variable control indicators. The research results show that the regression coefficient of BPO cost control construction on the revenue input of listed companies is 0.67, which obviously and effectively improves the company’s revenue ( Rd ) 13.21%; the regression coefficient of BPO cost control on financial risk (Fi) is -0.55, which reduces the financial risk of listed companies by 25.6%; the research demonstrates the necessity and feasibility of applying target BPO financial cost management for listed companies The study demonstrated the necessity and feasibility of applying target BPO financial cost management to listed companies, guaranteed the implementation of the target BPO cost management method to the ground, put forward relevant safeguard measures and suggestions for possible problems in the current application of target cost management, fundamentally solved the problem of enterprise financial cost control, and at the same time provided a guiding reference for the application of target BPO cost management in SMEs.

We consider continuous time risk processes in which the claim sizes are dependent and non-identically distributed phase-type distributions. The class of distributions we propose is easy to characterize and allows to incorporate the dependence between claims in a simple and intuitive way. It is also designed to facilitate the study of the risk processes by using a Markov-modulated fluid embedding technique. Using this technique, we obtain simple recursive procedures to determine the joint distribution of the time of ruin, the deficit at ruin and the number of claims before the ruin. We also obtain some bounds for the ultimate ruin probability. Finally, we provide a few examples of multivariate phase-type distributions and use them for numerical illustration. [ABSTRACT FROM AUTHOR]

This paper addresses the prediction of the total damage costs brought on by a drought episode under the French "Régime de Catastrophes Naturelles". Due to the specificity of this natural disaster compensation scheme, an early prediction of the cost of a disaster is needed to improve strategic decisions. Taking advantage of the access, thanks to a partnership with the Mission Risques Naturels, to a database of natural disaster claims fed by the major French insurance companies, we combine the information of drought event claims contained in this database with meteorological and socioeconomic data to achieve a more comprehensive knowledge of the exposure. Our prediction approach relies on the comparison of different statistical models and machine learning algorithms. To improve the prediction performance, we propose an aggregation of the different models. Since the main difficulty encountered is imbalanced data as a large majority of cities are not affected by a drought event, the predictions are assessed by F1-scores and Precision and Recall curves. [ABSTRACT FROM AUTHOR]

In this paper we consider a reinsurance strategy which combines a proportional and an excess-of-loss reinsurance in a risk model with multiple dependent classes of insurance business. Under the assumption that the claim number of the classes has a multivariate Poisson distribution, the aim is to maximize the expected utility of terminal wealth. In a general setting, after deriving the corresponding Hamilton–Jacobi–Bellman equation, we prove a Verification Theorem and identify sufficient conditions for the optimality. Then, in a special case with exponential utility, an explicit solution is found by solving an intricate associated static constrained optimization problem. [ABSTRACT FROM AUTHOR]

Consider a multidimensional discrete-time risk model in terms of some dependence structure. For the case of multivariate regularly varying claims, we study the asymptotic behavior of the ruin probabilities determined by some ruin sets. The estimates hold uniformly for all time horizons. Then we focus on a ruin set that allows partial capital transfers. As an application, the optimal allocation of the initial reserve is obtained. Some numerical simulations are presented to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we aim to discuss an axiom system for capital allocation with multivariate risk statistics. First, we introduce a class of multivariate risk statistics satisfying the properties of positive homogeneity and subadditivity, and provide the representations. Second, the axiom system of capital allocation with multivariate risk statistics are discussed. Specifically, the existence and the uniqueness of the capital allocation principles with positively homogeneous and subadditive risk statistics are studied. Finally, examples are also given to illustrate the proposed axioms for capital allocation with multivariate risk statistics, where the explicit capital allocation principles are derived for two kinds of multivariate risk statistics based on mean and standard deviation. The proposed capital allocations with multivariate risk statistics directly base on the samples of the random vectors, and thus they are more tractable than those with multivariate risk measures. [ABSTRACT FROM AUTHOR]

The optimisation criterion for dividends from a risky business is most often formalised in terms of the expected present value of future dividends. That criterion disregards a potential, explicit demand for the stability of dividends. In particular, within actuarial risk theory, the maximisation of future dividends has been studied as the so-called de Finetti problem. However, there the optimal strategies typically become so-called barrier strategies. These are far from stable, and suboptimal affine dividend strategies have recently received attention. In contrast, in the class of linear-quadratic problems, the demand for stability is explicitly stressed. These have often been studied in diffusion models different from the actuarial risk models. We bridge the gap between these thinking patterns by deriving optimal affine dividend strategies under a linear-quadratic criterion for an additive process. We characterise the value function by the Hamilton-Jacobi-Bellman equation, solve it, and compare the objective and the optimal controls to the classical objective of maximising the expected present value of future dividends. Thereby we provide a framework within which stability of dividends from a risky business, e.g. in classical risk theory, is explicitly demanded and obtained. [ABSTRACT FROM AUTHOR]

The stop-loss moments have generally been used as useful summary measures for analyzing the data which exceeds specific threshold levels. In many scientific studies, the investigator cannot record the sampling units with equal probability, and in such a scenario, the selected sample units appear with unequal probability, in other words with different weights, which leads to a biased or weighted sampling. In the present study, we examine the usefulness of stop-loss moments in biased sampling. The application of the weighted stop-loss moments in analyzing biased data has been investigated and compared using different empirical estimators through simulated and real data sets. [ABSTRACT FROM AUTHOR]

A behavioral mean-risk portfolio selection problem in continuous time is formulated and studied in this article. Based on the standard mean-variance portfolio selection problem, the cumulative distribution function of the cash flow is distorted by a probability distortion function. This probability distortion function represents the risk preference in a different way. Then the problem is no longer a convex optimization problem. This feature distinguishes it from the conventional linear-quadratic (LQ) problems. The stochastic optimal LQ control theory no longer applies. We take the quantile function of the terminal cash flow as the decision variable. The corresponding optimal terminal cash flow can be recovered by the optimal quantile function. Then the efficient strategy is the hedging strategy of the optimal terminal cash flow. [ABSTRACT FROM AUTHOR]

The classical Cramér–Lundberg model was the first attempt to describe the financial condition of the insurance company. The incomes were approximated by a steady stream of money, and insurance payments were not limited and could take any value from zero to infinity. The society did not invest any part of its money and does not have any employees, shareholders, or enterprise maintenance costs. There exist many modifications of the Cramér–Lundberg model that cover at least some of the problems described here but usually require insight into the internal financial policy of the insurance company. We propose another modification based on Markov processes defined by generalized convolutions. Thanks to the generalized convolutions, we can stochastically approximate the internal financial policy of the company based on publicly available data. In this paper, we focus on computing the ruin probability in the Cramér–Lundberg model for an infinite time horizon for the Markov processes where the transition probabilities are defined by generalized convolutions, in particular, by the α-convolution, maximal convolution, or Kendall convolution. [ABSTRACT FROM AUTHOR]

In this paper, we consider a company whose assets and liabilities evolve according to a correlated bivariate geometric Brownian motion, such as in Gerber and Shiu [(2003). Geometric Brownian motion models for assets and liabilities: From pension funding to optimal dividends. North American Actuarial Journal 7(3), 37–56]. We determine what dividend strategy maximises the expected present value of dividends until ruin in two cases: (i) when shareholders won't cover surplus shortfalls and a solvency constraint [as in Paulsen (2003). Optimal dividend payouts for diffusions with solvency constraints. Finance and Stochastics 7(4), 457–473] is consequently imposed and (ii) when shareholders are always to fund any capital deficiency with capital (asset) injections. In the latter case, ruin will never occur and the objective is to maximise the difference between dividends and capital injections. Developing and using appropriate verification lemmas, we show that the optimal dividend strategy is, in both cases, of barrier type. Both value functions are derived in closed form. Furthermore, the barrier is defined on the ratio of assets to liabilities, which mimics some of the dividend strategies that can be observed in practice by insurance companies. The existence and uniqueness of the optimal strategies are shown. Results are illustrated. [ABSTRACT FROM AUTHOR]

We study the busy period of a single server queueing system operating in two alternating modes - working and vacation. In the two modes the systems run as an M X / G / 1 queue with disasters, but with different parameters. The vacation mode starts once the number of customers drops to zero. It is terminated randomly (when it is not empty) with a transition to the working mode. At such a transition moment all the customers are transferred to the working mode; the service of the customer being served is lost and it starts from scratch in the working mode. Every busy period starts with a batch arrival into an empty system and terminates at the first time that the number of customers drops to zero. The working and the vacation periods are analyzed too. Finally, we apply the results to obtain the probability generating functions of the number of customers in the working, as well as in the vacation periods. [ABSTRACT FROM AUTHOR]

In this article, we consider an extended dual risk model under a mixed dividend strategy, which is a combination of ratcheting dividend strategy and periodic dividend strategy. The expected present value of dividends paid up to ruin is studied by using Lévy fluctuation theory, and its accurate expression is given in terms of scale functions. Numerical analysis under three different gain distributions is given for characterizing the impact of parameters on the expected present value of dividends paid up to ruin. [ABSTRACT FROM AUTHOR]

We propose a bottom-up quantitative reverse stress testing framework that identifies forward-looking fragilities tailored to a bank's portfolio, credit and funding strategies, models, and calibration constraints. Thus, instead of relying on historical events, we run a Monte Carlo simulation, and we mine those future states that contribute the most to a bank's cost of capital expressed in terms of scenario differential. This approach allows identifying both the systemic and idiosyncratic weaknesses of the bank's portfolio, with applications that include solvency risk, extreme events hedging, liquidity risk management, trading and credit limits, model validation and model risk management. [ABSTRACT FROM AUTHOR]