We give a short introduction to the stochastic calculus for ItôLévy processes and review briefly the two main methods of optimal control of systems described by such processes: (i) Dynamic programming and the Hamilton-Jacobi-Bellman (HJB) equation (ii) The stochastic maximum principle and its associated backward stochastic differential equation (BSDE). The two methods are illustrated by applica...

Mathematical mean-field approaches play an important role in different fields of Physics and Chemistry, but have found in recent works also their application in Economics, Finance and Game Theory. The objective of our paper is to study a special mean-field problem in a purely stochastic approach. We consider a stochastic differential equation that describes the dynamics of a particle X(N) influ...

This paper utilizes a game-theoretic model to analyze the disincentive effects of lowtuition policies on student effort. The model of parent and student responses to tuition subsidies is then calibrated using information from the High School and Beyond: Sophomore Cohort: 1980-92 and the National Longitudinal Survey of Youth 1979 data sets. The findings are that subsidizing tuition increases enr...

The Kelly framework is the natural multi-period extension of one-period mean-variance model Markowitz in sense that efficient frontier characterized by trading strategies having maximal instantaneous Sharpe ratio. We show traders naturally trade such a way as to induce an equilibrium for covariance matrix. This equilibrium, arising from alone, has property correlation can be described saddle po...

it is known that a stochastic dierential equation (sde) induces two probabilisticobjects, namely a diusion process and a stochastic ow. while the diusion process isdetermined by the in nitesimal mean and variance given by the coecients of the sde,this is not the case for the stochastic ow induced by the sde. in order to characterize thestochastic ow uniquely the in nitesimal covariance give...

A Dynkin game is considered for stochastic differential equations with random coefficients. We first apply Qiu and Tang’s maximum principle for backward stochastic partial differential equations to generalize Krylov estimate for the distribution of a Markov process to that of a non-Markov process, and establish a generalized Itô-Kunita-Wentzell’s formula allowing the test function to be a rando...

In this paper we study zero-sum two-player stochastic differential games with the help of theory of Backward Stochastic Differential Equations (BSDEs). At the one hand we generalize the results of the pioneer work of Fleming and Souganidis [8] by considering cost functionals defined by controlled BSDEs and by allowing the admissible control processes to depend on events occurring before the beg...

A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game. Mathematics Subject Classificati...