Related papers: Utility Maximization Problem with Uncertainty and …
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
We consider a stochastic optimal control problem in a market model with temporary and permanent price impact, which is related to an expected utility maximization problem under finite fuel constraint. We establish the initial condition…
In this paper we consider the maximum principle of optimal control for a stochastic control problem. This problem is governed by a system of fully coupled multi-dimensional forward-backward doubly stochastic differential equation with…
The dynamic concave utility (or the dynamic convex risk measure) of an unbounded endowment is studied and represented as the value process in the unique solution of a backward stochastic differential equation (BSDE) with an unbounded…
A robust control problem is considered in this paper, where the controlled stochastic differential equations (SDEs) include ambiguity parameters and their coefficients satisfy non-Lipschitz continuous and non-linear growth conditions, the…
We consider a utility maximization problem for an investment-consumption portfolio when the current utility depends also on the wealth process. Such kind of problems arise, e.g., in portfolio optimization with random horizon or with random…
We study an optimal investment problem under contagion risk in a financial model subject to multiple jumps and defaults. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the…
We consider a multi-period stochastic control problem where the multivariate driving stochastic factor of the system has known marginal distributions but uncertain dependence structure. To solve the problem, we propose to implement the…
In this paper, we study a Backward Stochastic Differential Equation with Jumps (BSDEJs in short) where the jumps have infinite activity. Following a forward approach based on Exponential Quadratic semimartingale, we prove the existence of…
In this work we consider the exponential utility maximization problem in the framework of semistatic hedging.
We consider an infinite dimensional optimization problem motivated by mathematical economics. Within the celebrated "Arbitrage Pricing Model", we use probabilistic and functional analytic techniques to show the existence of optimal…
We propose a new approach to solving dynamic decision problems with rewards that are unbounded below. The approach involves transforming the Bellman equation in order to convert an unbounded problem into a bounded one. The major advantage…
The present paper studies a kind of robust optimization problems with constraint. The problem is formulated through Backward Stochastic Differential Equations (BSDEs) with quadratic generators. A necessary condition is established for the…
In this paper we investigate a kind of optimal control problem of coupled forward-backward stochastic system with jumps whose cost functional is defined through a coupled forward-backward stochastic differential equation with Brownian…
We study relaxed stochastic control problems where the state equation is a one dimensional linear stochastic differential equation with random and unbounded coefficients. The two main results are existence of an optimal relaxed control and…
In this paper, we study a stochastic optimal control problem with stochastic volatility. We prove the sufficient and necessary maximum principle for the proposed problem. Then we apply the results to solve an investment, consumption and…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
In this paper, we consider a multi-attribute decision making problem where the decision maker's (DM's) objective is to maximize the expected utility of outcomes but the true utility function which captures the DM's risk preference is…
We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a num\'eraire-based semi-static utility maximization problem with an exponential utility preference. The randomization…
In this paper, we study a class of real-valued mean-field backward stochastic differential equations (BSDEs) with generators of quadratic growth in the control variable and the mean-field term. Under this assumption, together with a bounded…