We study an infinite horizon optimal stopping Markov problem which is either undiscounted (total reward) or with a general Markovian discount rate. Using ergodic properties of the underlying Markov process, we establish the feasibility of the stopping problem and prove the existence of optimal...

Investors tend to move funds when they are unhappy with their current portfolio managers' performance. We study the effect of the size of this flow of funds in an agent-based model of the financial market. The model combines the discrete choice approach from agent-based modelling, where all...

This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depend on an external process of economic factors. There are transaction costs with a structure that covers, in particular, the case of fixed plus...

This paper aims to open a new avenue for research in continuoustime financial market models with endogenous prices and heterogenous investors. The main result is the derivation of the limit of a discretetime evolutionary stock market model as the length of the time period tends to zero. The...

This paper studies the wealth dynamics of investors holding self-financing portfolios in a continuous-time model of a financial market. Asset prices are endogenously determined by market clearing. We derive results on the asymptotic dynamics of the wealth distribution and asset prices for...

We explore properties of the value function and existence of optimal stopping times for functionals with discontinuities related to the boundary of an open (possibly unbounded) set . The stopping horizon is either random, equal to the first exit from the set , or fixed (finite or infinite). The...

This tutorial is an introduction to the theory of viscosity solutions of Hamilton-Jacobi-Bellman equations/inequalities in the realm of stochastic control problems. It is an easy to use reference for application-oriented users of this theory. The presentation is based mainly on the book Pham...

This paper introduces a general continuous-time mathematical framework for solution of dynamic mean-variance control problems. We obtain theoretical results for two classes of functionals: the first one depends on the whole trajectory of the controlled process and the second one is based on its...

The timing of strategic exit is one of the most important but difficult business decisions, especially under competition and uncertainty. Motivated by this problem, we examine a stochastic game of exit in which players are uncertain about their competitor's exit value. We construct an...