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This article presents a class of Stackelberg mean-field-type games with multiple leaders and multiple followers. The decision-makers act in sequential order with informational differences. The state dynamics is driven by jump-diffusion processes and the cost function is non-quadratic and has a polynomial structure. The structures of Stackelberg strategies and costs of the leaders and followers are given in a semi-explicit way in state-and- mean-fieldtype feedback form. A sufficiency condition is provided using an infinite dimensional partial integro-differential system. The methodology is extended to multi-level hierarchical systems. It is shown that not only the set of decision-makers per level matters but also the number of hierarchical levels plays a key role in the global performance of the system. We also identify specific range of parameters for which the Nash equilibrium coincides with the hierarchical solution independently of the number of layers and the order of play., QC 20210720

This work examines the solvability of fractional conditional mean-field-type games. The evolution of the state is described by a time-fractional stochastic dynamics driven by jump-diffusion-regime switching Gauss-Volterra processes which include fractional Brownian motion and multi-fractional Brownian motion. The cost functional is non-quadratic and includes a fractional-integral of an higher order polynomial. We provide semi-explicitly the equilibrium strategies in state-and-conditional mean-field-type feedback form for all decision-makers., QC 20200702

In this paper, we investigate a credit rating problem based on the network of trading information (NoTI). First, several popular tools, such as assortativity analysis, community detection and centrality measurement, are introduced for analyzing the topology structures and properties of the NoTI. Then, the correlation between the characteristics of the network and the credit ratings is investigated to illustrate the feasibility of credit risk analysis based on the NoTI. Sovereign rating based on the world trade network is analyzed as a case study. The correlation between the centrality metrics and the sovereign ratings conducted by Standard & Poor's clearly shows that highly ranked economies with vigorous economic trading links usually have higher credit ratings. Finally, a simulation is conducted to illustrate the degree of improvement in credit rating prediction accuracy if the NoTI is considered as an additional attribute., QC 20190904

We establish existence of Markov chains of mean-field type with unbounded jump intensities by means of a fixed point argument using the total variation distance. We further show existence of nearly-optimal controls and, using a Markov chain backward SDE approach, we suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by such Markov chains of mean-field type., Not duplicate with DiVA 1269929QC 20230202

Point and interval estimation of future disability inception and recovery rates is predominantly carried out by combining generalized linear models with time series forecasting techniques into a two-step method involving parameter estimation from historical data and subsequent calibration of a time series model. This approach may lead to both conceptual and numerical problems since any time trend components of the model are incoherently treated as both model parameters and realizations of a stochastic process. We suggest that this general two-step approach can be improved in the following way: First, we assume a stochastic process form for the time trend component. The corresponding transition densities are then incorporated into the likelihood, and the model parameters are estimated using the Expectation-Maximization algorithm. We illustrate the modeling procedure by fitting the model to Swedish disability claims data., QC 20180618

We extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram [Transp. Res. B: Methodol., 45 (2011), pp. 1572–1589] to allow for nonlocal crowd aversion and arbitrarily but finitely many interacting crowds. The new crowd aversion feature grants pedestrians a “personal space” where crowding is undesirable. We derive the model from a particle picture and treat it as a mean-field type game. Solutions to the mean-field type game are characterized via a Pontryagin-type maximum principle. The behavior of pedestrians acting under nonlocal crowd aversion is illustrated by a numerical simulation., QC 20180320

We establish existence of Markov chains of mean-field type with unbounded jump intensities by means of a fixed point argument using the Total Variation distance. We further show existence of nearly-optimal controls and, using a Markov chain backward SDE approach, we suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by such Markov chains of mean-field type., QC 20181212

QC 20171102

We propose a functional version of the Hodrick-Prescott filter for functional data which take values in an infinite-dimensional separable Hilbert space. We further characterize the associated optimal smoothing operator when the associated linear operator is compact and the underlying distribution of the data is Gaussian., QC 20170509

A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some engineering applications of mean-field-type games including road traffic networks, multi-level building evacuation, millimeter wave wireless communications, distributed power networks, virus spread over networks, virtual machine resource management in cloud networks, synchronization of oscillators, energy-efficient buildings, online meeting and mobile crowdsensing., QC 20210927

We propose a functional version of the Hodrick–Prescott filter for functional data which take values in an infinite-dimensional separable Hilbert space. We further characterize the associated optimal smoothing operator when the associated linear operator is compact and the underlying distribution of the data is Gaussian.

We study a version of the functional Hodrick-Prescott filter in the case when the associated operator is not necessarily compact but merely closed and densely defined with closed range. We show that the associated optimal smoothing operator preserves the structure obtained in the compact case when the underlying distribution of the data is Gaussian., QC 20160519

This work introduces a simple mean-field network game that captures some of the key dynamic features of crowd and pedestrian flows in multi-level building evacuations. It considers a route choice by finite number of strategic agents. Each agent state is represented by a simple first order dynamical system. Each agent measures its local congestion measure based on its location in the building. Including the local congestion term and its evolution along the path causes a sort of dispersion of the flow: the agents will try to avoid high density areas in order to reduce their overall walking costs and queuing cost at the exits. Each agent will move to one the closest exits that is safer and that has less congestion through the path. The dynamics of lower layer floors are influenced not only by the agents in that floor but also by the incoming flow from the upper layers through the stairs leading to interacting flows between the floors. Numerics and simulations are carried out to illustrate mean-field equilibria of the evacuation process., QC 20161129

We consider large insurance portfolios consisting of life or disability insurance policies that are assumed independent, conditional on a stochastic process representing the economic-demographic environment. Using the conditional law of large numbers, we show that when the portfolio of liabilities becomes large enough, its value on a delta-year horizon can be approximated by a functional of the environment process. Based on this representation, we derive a semi-analytical approximation of the systematic risk quantiles of the future liability value for a homogeneous portfolio when the environment is represented by a one-factor diffusion process. For the multi-factor diffusion case, we propose two different risk aggregation techniques for a portfolio consisting of large, homogeneous pools. We give numerical results comparing the resulting capital charges with the Solvency II standard formula, based on disability claims data from the Swedish insurance company Folksam., QC 20161019

We propose a stochastic semi-Markovian framework for disability modelling in a multi-period discrete-time setting. The logistic transforms of disability inception and recovery probabilities are modelled by means of stochastic risk factors and basis functions, using counting processes and generalized linear models. The model for disability inception also takes IBNR claims into consideration. We fit various versions of the models into Swedish disability claims data., QC 20150113. Updated from e-pub ahead of print.

We study a general class of nonlinear second-order variational inequalities with interconnected bilateral obstacles, related to a multiple modes switching game. Under rather weak assumptions, using systems of penalized unilateral backward SDEs, we construct a continuous viscosity solution of polynomial growth. Moreover, we establish a comparison result which in turn yields uniqueness of the solution., QC 20150508

We formulate and solve a finite horizon full balance sheet of a two-mode optimal switching problem related to trade-off strategies between expected profit and cost yields. Given the current mode, this model allows for either a switch to the other mode or termination of the project, and this happens for both sides of the balance sheet. A novelty in this model is that the related obstacles are nonlinear in the underlying yields, whereas, they are linear in the standard optimal switching problem. The optimal switching problem is formulated in terms of a system of Snell envelopes for the profit and cost yields which act as obstacles to each other. We prove the existence of a continuous minimal solution of this system using an approximation scheme and fully characterize the optimal switching strategy., QC 20150918

In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the valuefunction imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng's type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models., QC 20160126

We consider the problem of switching a large number of production lines between two modes, high-production and low-production. The switching is based on the optimal expected profit and cost yields of the respective production lines, and considers both sides of the balance sheet. Furthermore, the production lines are all assumed to be interconnected through a coupling term, which is the average of all optimal expected yields. Intuitively, this means that each individual production line is compared to the average of all its peers which acts as a benchmark. Due to the complexity of the problem, we consider the aggregated optimal expected yields, where the coupling term is approximated with the mean of the optimal expected yields. This turns the problem into a two-modes optimal switching problem of mean-field type, which can be described by a system of Snell envelopes where the obstacles are interconnected and nonlinear. The main result of the paper is a proof of a continuous minimal solution to the system of Snell envelopes, as well as the full characterization of the optimal switching strategy., Updated from "Manuscript" to "Article". QC 20150918

We suggest an optimality criterion, for choosing the best smoothing parameters for an extension of the so-called Hodrick-Prescott Multivariate (HPMV) filter. We show that this criterion admits a whole set of optimal smoothing parameters, to which belong the widely used noise-to-signal ratios. We also propose explicit consistent estimators of these noise-to-signal ratios, which in turn yield a new performant method to estimate the output gap., QC 20110503