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This study examines the balanced Maruyama with two step approximations of stochastic Hopffeld neural networks with delay. The main aim of this paper is to discover the conditions under which the exact solutions remain stable for the balanced Maruyama with two-step approximations of stochastic delay Hopfield neural networks (SDHNN). The semi-martingale theorem for convergence is used to demonstrate the almost sure exponential stability of balanced Maruyama with two-step approximations of stochastic delay Hofield networks. Additionally, the numerical balanced Euler approximation's stability conditions are compared. Our theoretical findings are illustrated with numerical experiments. [ABSTRACT FROM AUTHOR]

What is absence of arbitrage for non-discounted prices? How can one define this so that it does not change meaning if one decides to discount after all? The answer to both questions is a new discounting-invariant no-arbitrage concept. As in earlier work, we define absence of arbitrage as the zero strategy or some basic strategies being maximal. The key novelty is that maximality of a strategy is defined in terms of share holdings instead of value. This allows us to generalise both NFLVR, by dynamic share efficiency, and NUPBR, by dynamic share viability. These new concepts are the same for discounted or undiscounted prices, and they can be used in general models under minimal assumptions on asset prices. We establish corresponding versions of the FTAP, i.e., dual characterisations in terms of martingale properties. As one expects, "properly anticipated prices fluctuate randomly", but with an endogenous discounting process which cannot be chosen a priori. An example with N geometric Brownian motions illustrates our results. [ABSTRACT FROM AUTHOR]

In this paper we provide an Itô-Tanaka trick formula in a non semimartingale context, filling a gap in the theory of regularisation by noise. In a classical Brownian framework, the Itô-Tanaka trick links the time average of a function f along the solution to a Brownian SDE, with the solution of a Fokker-Planck PDE. Our main contribution is to provide such a link in a non-semimartingale framework, where the solution to the non-available PDE is replaced by a well-chosen random field. This allows us to improve well-posedness results for fractional SDEs with a singular drift coefficient. [ABSTRACT FROM AUTHOR]

In this paper, we studied the particular cases of higher-order realized multipower variation process, their asymptotic properties comprising the probability limits and limit distributions were highlighted. The respective asymptotic variances of the limit distributions were obtained and jump detection models were developed from the asymptotic results. The models were obtained from the particular cases of the higher-order of the realized multipower variation process, in a class of continuous stochastic volatility semimartingale process. These are extensions of the method of jump detection by Barndorff-Nielsen and Shephard (2006), for large discrete data. An Empirical Application of the models to the Nigerian All Share Index (NASI) data shows that the models are robust to jumps and suggest that stochastic models with added jump components will give a better representation of the NASI price process. [ABSTRACT FROM AUTHOR]

We consider families of equivalent probability measures Q with a property related to concepts known in the literature under different names such as rectangularity or multiplicative stability. For the problems considered in this paper such a property yields dynamical consistency. We prove under a weak-compactness assumption with general filtrations and continuous processes that all semimartingales have an additive decomposition as the sum of a predictable non-decreasing process and a universal local supermartingale, by this concept we mean a process that is a local supermartingale with respect to each element of Q. We also show that processes having a supermartingale property with respect to a superadditive nonlinear conditional expectation associated to the family Q are always semimartingales under weak-compactness. These results are relevant in stochastic optimization problems including optimal stopping under model ambiguity. [ABSTRACT FROM AUTHOR]

Abstract We develop a nonparametric estimator for the spectral density of a bivariate pure-jump Itô semimartingale from high-frequency observations of the process on a fixed time interval with asymptotically shrinking mesh of the observation grid. The process of interest is locally stable, i.e., its Lévy measure around zero is like that of a time-changed stable process. The spectral density function captures the dependence between the small jumps of the process and is time invariant. The estimation is based on the fact that the characteristic exponent of the high-frequency increments, up to a time-varying scale, is approximately a convolution of the spectral density and a known function depending on the jump activity. We solve the deconvolution problem in Fourier transform using the empirical characteristic function of locally studentized high-frequency increments and a jump activity estimator. [ABSTRACT FROM AUTHOR]

Abstract The estimation of a class of continuous, convergent semimartingales, observed via a linear sensor is considered. In particular, conditions securing the consistency of the Bayesian estimator are established. These are in the form of a Persistence of Excitation (PE) property. This PE condition is stronger than the one required in the case of the estimation of a constant random vector. It coincides with the latter, when the partially observed semimartingale has a finite quadratic variation over [ 0 , ∞ ]. The paper is concluded with two Systems and Control application examples. [ABSTRACT FROM AUTHOR]

It is shown that every adapted Brownian bridge on a geodesically complete connected Riemannian manifold is a semimartingale including its terminal time, without any further assumptions on the geometry. In particular, it follows that every such process can be horizontally lifted to a smooth principal fiber bundle with connection, including its terminal time. The proof is based on a localized Hamilton-type gradient estimate. [ABSTRACT FROM AUTHOR]

In this paper we discuss weak convergence of continuous-time Markov chains to a non-symmetric pure jump process. We approach this problem using Dirichlet forms as well as semimartingales. As an application, we discuss how to approximate a given Markov process by Markov chains. [ABSTRACT FROM AUTHOR]

Abstract In applications the properties of a stochastic feature often change gradually rather than abruptly, that is: after a constant phase for some time they slowly start to vary. In this paper we discuss statistical inference for the detection and the localization of gradual changes in the jump characteristic of a discretely observed Ito semimartingale. We propose a new measure of time variation for the jump behaviour of the process. The statistical uncertainty of a corresponding estimate is analysed by deriving new results on the weak convergence of a sequential empirical tail integral process and a corresponding multiplier bootstrap procedure. [ABSTRACT FROM AUTHOR]

We consider high-frequency observations from a fractional Brownian motion. Inspired by the work of Jean Jacod in a diffusion setting, we investigate the asymptotic behavior of various classical statistics related to the local times of the process. We show that as in the diffusion case, these statistics indeed converge to some local times up to a constant factor. As a corollary, we provide limit theorems for the quadratic variation of the absolute value of a fractional Brownian motion. [ABSTRACT FROM AUTHOR]

We consider a Brownian semimartingale X (the sum of a stochastic integral w.r.t. a Brownian motion and an integral w.r.t. Lebesgue measure), and for each n an increasing sequence T (n, i) of stopping times and a sequence of positive ℱ T (n, i) -measurable variables Δ (n, i) such that S (n, i) : = T (n, i) + Δ (n, i) ≤ T (n, i + 1). We are interested in the limiting behavior of processes of the form U t n (g) = δ n ∑ i : S (n, i) ≤ t [ g (T (n, i), ξ i n) − α i n (g) ], where δ n is a normalizing sequence tending to 0 and ξ i n = Δ (n, i) − 1 / 2 (X S (n, i) − X T (n, i)) and α i n (g) are suitable centering terms and g is some predictable function of (ω, t, x). Under rather weak assumptions on the sequences T (n, i) as n goes to infinity, we prove that these processes converge (stably) in law to the stochastic integral of g w.r.t. a random measure B which is, conditionally on the path of X, a Gaussian random measure. We give some applications to rates of convergence in discrete approximations for the p -variation processes and local times. [ABSTRACT FROM AUTHOR]

Abstract: We propose an approach to the valuation of payoffs in general semimartingale models of financial markets where prices are nonnegative. Each asset price can hit 0; we only exclude that this ever happens simultaneously for all assets. We start from two simple, economically motivated axioms, namely, absence of arbitrage (in the sense of NUPBR) and absence of relative arbitrage among all buy‐and‐hold strategies (called static efficiency). A valuation process for a payoff is then called semi‐efficient consistent if the financial market enlarged by that process still satisfies this combination of properties. It turns out that this approach lies in the middle between the extremes of valuing by risk‐neutral expectation and valuing by absence of arbitrage alone. We show that this always yields put‐call parity, although put and call values themselves can be nonunique, even for complete markets. We provide general formulas for put and call values in complete markets and show that these are symmetric and that both contain three terms in general. We also show that our approach recovers all the put‐call parity respecting valuation formulas in the classic theory as special cases, and we explain when and how the different terms in the put and call valuation formulas disappear or simplify. Along the way, we also define and characterize completeness for general semimartingale financial markets and connect this to the classic theory. [ABSTRACT FROM AUTHOR]

Limit theory with stochastic integrals plays a major role in time series econometrics. In earlier contributions on weak convergence to stochastic integrals, the literature commonly uses martingale and semi-martingale structures. Liang, Phillips, Wang, and Wang (2016) (see also Wang (2015), Chap. 4.5) currently extended weak convergence to stochastic integrals by allowing for a linear process or a α -mixing sequence in innovations. While these martingale, linear process and α -mixing structures have wide relevance, they are not sufficiently general to cover many econometric applications that have endogeneity and nonlinearity. This paper provides new conditions for weak convergence to stochastic integrals. Our frameworks allow for long memory processes, causal processes, and near-epoch dependence in innovations, which have applications in a wide range of econometric areas such as TAR, bilinear, and other nonlinear models. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the effects of noise on bipower variation, realized volatility (RV) and testing for co‐jumps in high‐frequency data under the small noise framework. We first establish asymptotic properties of bipower variation in this framework. In the presence of the small noise, RV is asymptotically biased, and the additional asymptotic conditional variance term appears in its limit distribution. We also propose consistent estimators for the asymptotic variances of RV. Second, we derive the asymptotic distribution of the test statistic proposed in (Ann. Stat. 37, 1792‐1838) under the presence of small noise for testing the presence of co‐jumps in a two‐dimensional Itô semimartingale. In contrast to the setting in (Ann. Stat. 37, 1792‐1838), we show that the additional asymptotic variance terms appear and propose consistent estimators for the asymptotic variances in order to make the test feasible. Simulation experiments show that our asymptotic results give reasonable approximations in the finite sample cases. [ABSTRACT FROM AUTHOR]

We study the optimal discretization error of stochastic integrals, driven by a multidimensional continuous Brownian semimartingale. In this setting we establish a pathwise lower bound for the renormalized quadratic variation of the error and we provide a sequence of discretization stopping times, which is asymptotically optimal. The latter is defined as hitting times of random ellipsoids by the semimartingale at hand. In comparison with previous available results, we allow a quite large class of semimartingales (relaxing in particular the non degeneracy conditions usually requested) and we prove that the asymptotic lower bound is attainable. [ABSTRACT FROM AUTHOR]

This paper is devoted to comparison of strong solutions of stochastic equations with respect to optional semimartingales. Optional semimartingales have right and left limits but are not necessarily continuous and therefore defined on “unusual” probability spaces. Integration theory with respect to optional semimartingales is well-developed. However, not much attention is given to stochastic integral equations of optional semimartingales. A pathwise comparison result for strong solutions of a very general class of optional stochastic equations with non-lipshitz coefficients is given. Moreover, simple applications to mathematical finance is presented. [ABSTRACT FROM AUTHOR]

The functional Itô formula, firstly introduced by Bruno Dupire for continuous semimartingales, might be extended in two directions: different dynamics for the underlying process and/or weaker assumptions on the regularity of the functional. In this paper, we pursue the former type by proving the functional version of the Meyer–Tanaka formula. Following the idea of the proof of the classical time-dependent Meyer–Tanaka formula, we study the mollification of functionals and its convergence properties. As an example, we study the running maximum and the max-martingales of Yor and Obłój. [ABSTRACT FROM AUTHOR]

In the literature, the Euler-Maruyama (EM) method for approximation purposes of stochastic differential Equations (SDE) driven by α-stable Lévy motions is reported. Convergence in probability of that method was proven but it is surrounded by some ambiguities. To accomplish the but without ambiguities, this article has derived convergence in probability of numerical EM method based on diffusion given by semimartingales for SDEs driven by α-stable processes. Some examples are provided, their numerical solution are obtained and theoretical results are reconfirmed. The adopted method could be applied to other subclasses of semimartingales. [ABSTRACT FROM AUTHOR]

With rapid development of the global market, the number of financial securities has significantly grown, which greatly challenges the measuring of financial quantities. Among others, the estimation of covariance matrix which plays an important role in risk management becomes no longer accurate. In this paper, we consider the estimation of integrated covariance matrix of semi-martingales under framework of high dimension by using high frequency data. We assume that the multivariate asset prices are observed asynchronously and all the observed prices are contaminated by microstructure noise. We employ the pre-averaging method to remove the microstructure noise and the generalized synchronization method to deal with the non-synchronicity. Moreover, to avoid the inconsistency in the high-dimensional covariance matrix estimation, we propose a regularized estimate. The consistency under matrix ℓ2-norm is established. Compared to existing results, our estimator improves the accuracy of the estimation. Finally, we assess the theoretical results via some simulation studies. [ABSTRACT FROM AUTHOR]

We construct planar semimartingales that include the Walsh Brownian motion as a special case, and derive Harrison-- Shepp-type equations and a change-of-variable formula in the spirit of Freidlin--Sheu for these so-called "Walsh semimartingales". We examine the solvability of the resulting system of stochastic integral equations. In appropriate Markovian settings we study two types of connections to martingale problems, questions of uniqueness in distribution for such processes, and a few examples. [ABSTRACT FROM AUTHOR]

The sufficient conditions of the almost sure exponential stability of the exact solution for the stochastic pantograph differential equation are considered, with a Khasminskii-type condition. The almost sure exponential stability of the numerical solutions by the Euler–Maruyama method and the backward Euler–Maruyama method is also discussed, based on the discrete semimartingale convergence theorem. We present the sufficient conditions for the stability of the Euler–Maruyama method, with one extra condition when compared with the exact solution. We show that the backward Euler–Maruyama method can share almost the same conditions for the almost sure exponential stability as the exact solution. [ABSTRACT FROM AUTHOR]

We establish a noncommutative Blackwell-Ross inequality for supermartingales under a suitable condition which generalizes Khan's work to the noncommutative setting. We then employ it to deduce an Azuma-type inequality. [ABSTRACT FROM AUTHOR]

In this paper we relate the set of structure-preserving equivalent martingale measures Msp for financial models driven by semimartingales with conditionally independent increments to a set of measurable and integrable functions Y. More precisely, we prove thatMsp ≠ if and only if Y ≠ Φ, and connect the sets Msp and Y to the semimartingale characteristics of the driving process. As examples we consider integrated Lévy models with independent stochastic factors and time-changed Lévy models and derive mild conditions for Msp ≠ Φ. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a new estimator of the integrated volatility of Itô semimartingales in the presence of both market microstructure noise and jumps when sampling times are endogenous. In the first step, our estimation wipes off the effects of the microstructure noise, and in the second step our estimator shrinks the effects of jumps. We provide consistency of the estimator when the jumps have finite variation and infinite variation and establish a central limit theorem for the estimator in a general endogenous time setting when the jumps only have finite variation. Simulation illustrates the performance of the proposed estimator. [ABSTRACT FROM PUBLISHER]

In this work, for a reference filtration $\mathbb {F}$ , we develop a method for computing the semimartingale decomposition of $\mathbb {F}$ -martingales in a specific type of enlargement of $\mathbb {F}$ . As an application, we study the progressive enlargement of $\mathbb {F}$ with a sequence of non-ordered default times and show how to deduce results concerning the first-to-default, $k$ th-to-default, k-out-of- n-to-default or all-to-default events. In particular, using this method, we compute explicitly the semimartingale decomposition of $\mathbb {F}$ -martingales under the absolute continuity condition of Jacod. [ABSTRACT FROM AUTHOR]

The present paper accomplishes a major step towards a reconciliation of two conflicting approaches in mathematical finance: on the one hand, the mainstream approach based on the notion of no arbitrage (Black, Merton & Scholes), and on the other hand, the consideration of non-semimartingale price processes, the archetype of which being fractional Brownian motion (Mandelbrot). Imposing (arbitrarily small) proportional transaction costs and considering logarithmic utility optimisers, we are able to show the existence of a semimartingale, frictionless shadow price process for an exponential fractional Brownian financial market. [ABSTRACT FROM AUTHOR]

This article examines the leverage effect, or the generally negative covariation between asset returns and their changes in volatility, under a general setup that allows the log-price and volatility processes to be Itô semimartingales. We decompose the leverage effect into continuous and discontinuous parts and develop statistical methods to estimate them. We establish the asymptotic properties of these estimators. We also extend our methods and results (for the continuous leverage) to the situation where there is market microstructure noise in the observed returns. We show in Monte Carlo simulations that our estimators have good finite sample performance. When applying our methods to real data, our empirical results provide convincing evidence of the presence of the two leverage effects, especially the discontinuous one. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We study the existence, uniqueness and stability of solutions of general stochastic differential equations with constraints driven by semimartingales and processes with bounded p -variation. Applications to SDEs with constraints driven by fractional Brownian motion and standard Brownian motion are given. [ABSTRACT FROM AUTHOR]

In this paper we examine the asymptotic theory for U-statistics and V-statistics of discontinuous Itô semimartingales that are observed at high frequency. For different types of kernel functions we show laws of large numbers and associated stable central limit theorems. In most of the cases the limiting process will be conditionally centered Gaussian. The structure of the kernel function determines whether the jump and/or the continuous part of the semimartingale contribute to the limit. [ABSTRACT FROM AUTHOR]

We study multivalued stochastic differential equations (MSDEs) with maximal monotone operators driven by semimartingales with jumps. We discuss in detail some methods of approximation of solutions of MSDEs based on discretization of processes and Yosida approximation of the monotone operator. We also study the general problem of stability of solutions of MSDEs with respect to the convergence of driving semimartingales. [ABSTRACT FROM AUTHOR]

In this paper, we consider the optimal approximation of a Rosenblatt process based on semimartingales of the formwhere (y1,y2)↦a(y1,y2) is a square integrable process andBis a standard Brownian motion. We show that there exists a unique semimartingale closest to Rosenblatt process ifais deterministic. [ABSTRACT FROM PUBLISHER]

Given an Itō semimartingale with a time-homogeneous jump part observed at high frequency, we prove weak convergence of a normalized truncated empirical distribution function of the Lévy measure to a Gaussian process. In contrast to competing procedures, our estimator works for processes with a non-vanishing diffusion component and under simple assumptions on the jump process. [ABSTRACT FROM AUTHOR]

We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very convenient in financial modelling in general. Especially it allows us to carefully discuss the question of well-definedness of semimartingale Libor models, whose construction crucially relies on a sequence of measure changes. [ABSTRACT FROM AUTHOR]

In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations with respect to semimartingale integrators. We present new connections between their solutions. In particular, we show that attainable sets of solutions to stochastic inclusions are subsets of values of multivalued solutions of certain set-valued stochastic equations. We also show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. The results obtained in the paper generalize results dealing with this topic known both in deterministic and stochastic cases. [ABSTRACT FROM AUTHOR]

In this paper, the Euler-Maruyama (EM) method with random variable stepsize is studied to reproduce the almost sure stability of the true solutions of stochastic differential equations. Since the choice of the time step is based on the current state of the solution, the time variable is proved to be a stopping time. Then the semimartingale convergence theory is employed to obtain the almost sure stability of the random variable stepsize EM solution. To our best knowledge, this is the first paper to apply the random variable stepsize (with clear proof of the stopping time) to the analysis of the almost sure stability of the EM method. [ABSTRACT FROM AUTHOR]

This paper deals with forward performances of HARA type. Precisely, for a market model in which stock price processes are modeled by a locally bounded d-dimensional semimartingale, we elaborate a complete and explicit characterization for this type of forward utilities. In particular, under some mild technical assumptions of integrability, we prove that the risk aversion process of a power-type forward utility is constant. Furthermore, the optimal portfolios for all HARA forward utilities are explicitly described. Our approach is based on the minimal Hellinger martingale densities that are obtained from the important statistical concept of Hellinger process. These martingale densities were introduced recently and appeared herein tailor-made for these forward utilities. After outlining our parametrization method for the HARA forward, we provide illustrations on discretetime market models. [ABSTRACT FROM AUTHOR]

When the planning horizon is long, and the safe asset grows indefinitely, isoelastic portfolios are nearly optimal for investors who are close to isoelastic for high wealth, and not too risk averse for low wealth. We prove this result in a general arbitrage-free, frictionless, semimartingale model. As a consequence, optimal portfolios are robust to the perturbations in preferences induced by common option compensation schemes, and such incentives are weaker when their horizon is longer. Robust option incentives are possible, but require several, arbitrarily large exercise prices, and are not always convex. [ABSTRACT FROM AUTHOR]

This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function. Two settings are considered. First, in a general semimartingale model where random endowments are present, a sequence of utilities defined on [ABSTRACT FROM AUTHOR]

We consider the portfolio choice problem for a long-run investor in a general continuous semimartingale model. We combine the decision criterion of pathwise growth optimality with a flexible specification of attitude toward risk, encoded by a linear drawdown constraint imposed on admissible wealth processes. We define the constrained numéraire property through the notion of expected relative return and prove that drawdown-constrained numéraire portfolio exists and is unique, but may depend on the investment horizon. However, when sampled at the times of its maximum and asymptotically as the time-horizon becomes distant, the drawdown-constrained numéraire portfolio is given explicitly through a model-independent transformation of the unconstrained numéraire portfolio. The asymptotically growth-optimal strategy is obtained as limit of numéraire strategies on finite horizons. [ABSTRACT FROM AUTHOR]

We consider an optimal investment problem with intermediate consumption and random endowment, in an incomplete semimartingale model of the financial market. We establish the key assertions of the utility maximization theory, assuming that both primal and dual value functions are finite in the interiors of their domains and that the random endowment at maturity can be dominated by the terminal value of a self-financing wealth process. In order to facilitate the verification of these conditions, we present alternative, but equivalent conditions, under which the conclusions of the theory hold. [ABSTRACT FROM AUTHOR]

This paper extends the long-term factorization of the stochastic discount factor introduced and studied by Alvarez and Jermann (2005) in discrete-time ergodic environments and by Hansen and Scheinkman (2009) and Hansen (2012) in Markovian environments to general semimartingale environments. The transitory component discounts at the stochastic rate of return on the long bond and is factorized into discounting at the long-term yield and a positive semimartingale that extends the principal eigenfunction of Hansen and Scheinkman (2009) to the semimartingale setting. The permanent component is a martingale that accomplishes a change of probabilities to the long forward measure, the limit of T-forward measures. The change of probabilities from the data-generating to the long forward measure absorbs the long-term risk-return trade-off and interprets the latter as the long-term risk-neutral measure. [ABSTRACT FROM AUTHOR]

We study the class of disentangled realized estimators for the integrated covariance matrix of Brownian semimartingales with finite activity jumps. These estimators separate correlations and volatilities. We analyze different combinations of quantile- and median-based realized volatilities, and four estimators of realized correlations with three synchronization schemes. Their finite sample properties are studied under five data generating processes, in presence, or not, of microstructure noise, and under synchronous and asynchronous trading. The main finding is that synchronizing with previous tick interpolation combined with the pre-averaged version of disentangled estimators based on Gaussian ranks (for the correlations) and median deviations (for the volatilities) provide a precise, computationally efficient, and easy alternative to measure integrated covariances. A minimum variance portfolio application shows the superiority of this disentangled realized estimator in terms of numerous performance metrics. [ABSTRACT FROM AUTHOR]

We combine stochastic control methods, white noise analysis, and Hida–Malliavin calculus applied to the Donsker delta functional to obtain explicit representations of semimartingale decompositions under enlargement of filtrations. Some of the expressions are more explicit than previously known. The results are illustrated by examples. [ABSTRACT FROM AUTHOR]

Nie and Rutkowski (Int. J. Theor. Appl. Finance 18:1550048, 2015; Math. Finance, 2016, to appear) examined fair bilateral pricing in models with funding costs and an exogenously given collateral. The main goal of this work is to extend results from Nie and Rutkowski (Int. J. Theor. Appl. Finance 18:1550048, 2015; Math. Finance, 2016, to appear) to the case of an endogenous margin account depending on the contract's value for the hedger and/or the counterparty. Comparison theorems for BSDEs from Nie and Rutkowski (Theory Probab. Appl., 2016, forthcoming) are used to derive bounds for unilateral prices and to study the range for fair bilateral prices in a general semimartingale model. The backward stochastic viability property, introduced by Buckdahn et al. (Probab. Theory Relat. Fields 116:485-504, 2000), is employed to examine the bounds for fair bilateral prices for European claims with a negotiated collateral in a diffusion-type model. We also generalize in several respects the option pricing results from Bergman (Rev. Financ. Stud. 8:475-500, 1995), Mercurio (Actuarial Sciences and Quantitative Finance, pp. 65-95, 2015) and Piterbarg (Risk 23(2):97-102, 2010) by considering contracts with cash-flow streams and allowing for idiosyncratic funding costs for risky assets. [ABSTRACT FROM AUTHOR]

In this Note, we present the weak convergence of additive functionals of processes with locally independent increments and Markov switching in Lévy and Poisson approximation schemes. The singular perturbation problem for the generators of switched processes is used to prove the semimartingales' predictable characteristics convergence. [ABSTRACT FROM AUTHOR]

This paper studies additive subordination, which we show is a useful technique for constructing time-inhomogeneous Markov processes with analytical tractability. This technique is a natural generalization of Bochner's subordination that has proved to be extremely useful in financial modeling. Probabilistically, Bochner's subordination corresponds to a stochastic time change with respect to an independent Lévy subordinator, while in additive subordination, the Lévy subordinator is replaced by an additive one. We generalize the classical Phillips theorem for Bochner's subordination to the additive subordination case, based on which we provide Markov and semimartingale characterizations for a rich class of jump-diffusions and pure jump processes obtained from diffusions through additive subordination, and obtain spectral decomposition for them. To illustrate the usefulness of additive subordination, we develop an analytically tractable cross-commodity model for spread option valuation that is able to calibrate the implied volatility surface of each commodity. Moreover, our model can generate implied correlation patterns that are consistent with market observations and economic intuitions. [ABSTRACT FROM AUTHOR]