Bayesian switching multiple disorder problems

The switching multiple disorder problem seeks to determine an ordered infinite sequence of times of alarms which are as close as possible to the unknown times of disorders, or change-points, at which the observable process changes its probability characteristics. We study a Bayesian formulation of this problem for an observable Brownian motion with switching constant drift rates. The method of proof is based on the reduction of the initial problem to an associated optimal switching problem for a three-dimensional diffusion posterior probability process and the analysis of the equivalent coupled parabolic-type free-boundary problem. We derive analytic-form estimates for the Bayesian risk function and the optimal switching boundaries for the components of the posterior probability process

A maximum principle for stochastic differential games with g-expectations and partial information

In this paper, we initiate a study on optimal control problem for stochastic differential games under generalized expectation via backward stochastic differential equations and partial information. We first prove a sufficient maximum principle for zero-sum stochastic differential game problems. And then extend our approach to general stochastic differential games (nonzero-sum games) and obtain an equilibrium point of such game. Finally, we give some examples of applications. This is an Accepted Manuscript of an article published by Taylor & Francis in Stochastics An International Journal of Probability and Stochastic Processes: formerly Stochastics and Stochastics Report

A MAXIMUM PRINCIPLE FOR STOCHASTIC DIFFERENTIAL GAMES WITH PARTIAL INFORMATION

In this paper we first deal with the problem of optimal control for zero-sum stochastic differential games. We give a necessary and sufficient maximum principle for that problem with partial information. Then we use the result to solve a problem in finance. Finally, we extend our approach to general stochastic games (nonzero-sum), and obtain an equilibrium point of such game

A Malliavin calculus approach to general stochastic differential games with partial information

In this paper we consider a general partial information stochastic differential game where the state process is a controlled Itô-Lévy process. We use Malliavin calculus to derive a maximum principle for general stochastic differential games. The results are applied to solve a worst case scenario portfolio problem in finance

A Maximum Principle Approach to Risk Indifference Pricing with Partial Information

We consider the problem of risk indifference pricing on an incomplete market, namely on a jump diffusion market where the controller has limited access to market information. We use the maximum principle for stochastic differential games to derive a formula for the risk indifference price of a European-type claimpublishedVersio