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Recently, there has been a growing interest in developing inventory control policies which are robust to model misspecification. One approach is to posit that nature selects a worst-case distribution for any stochastic primitives from some…
We give explicit solutions for utility maximization of terminal wealth problem $u(X_T)$ in the presence of Knightian uncertainty in continuous time $[0,T]$ in a complete market. We assume there is uncertainty on both drift and volatility of…
Two major financial market complexities are transaction costs and uncertain volatility, and we analyze their joint impact on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment…
In a continuous time stochastic economy, this paper considers the problem of consumption and investment in a financial market in which the representative investor exhibits a change in the discount rate. The investment opportunities are a…
We give a general formulation of the utility maximization problem under nondominated model uncertainty in discrete time and show that an optimal portfolio exists for any utility function that is bounded from above. In the unbounded case,…
We study Merton's expected utility maximization problem in an incomplete market, characterized by a factor process in addition to the stock price process, where all the model primitives are unknown. The agent under consideration is a price…
This paper introduces a new functional optimization approach to portfolio optimization problems by treating the unknown weight vector as a function of past values instead of treating them as fixed unknown coefficients in the majority of…
The "standard" Merton formulation of optimal investment and consumption involves optimizing the integrated lifetime utility of consumption, suitably discounted, together with the discounted future bequest. In this formulation the utility of…
In this paper, which is a continuation of the previously published discrete time paper we develop a theory for continuous time stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a…
This paper studies an optimal dividend problem for a company that aims to maximize the mean-variance (MV) objective of the accumulated discounted dividend payments up to its ruin time. The MV objective involves an integral form over a…
This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio…
We consider the problem of portfolio optimization in a simple incomplete market and under a general utility function. By working with the associated Hamilton-Jacobi-Bellman partial differential equation (HJB PDE), we obtain a closed-form…
This paper discusses a nonlinear integral equation arising from portfolio selection with a class of time-inconsistent preferences. We propose a unified framework requiring minimal assumptions, such as right-continuity of market coefficients…
We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected…
This paper presents a new framework for Merton's optimal investment problem which uses the theory of Meyer $\sigma$-fields to allow for signals that possibly warn the investor about impending jumps. With strategies no longer predictable,…
Classical portfolio optimization methods typically determine an optimal capital allocation through the implicit, yet critical, assumption of statistical time-invariance. Such models are inadequate for real-world markets as they employ…
This paper considers the Merton portfolio management problem. We are concerned with non-exponential discounting of time and this leads to time inconsistencies of the decision maker. Following Ekeland and Pirvu 2006, we introduce the notion…
We introduce a bond portfolio management theory based on foundations similar to those of stock portfolio management. A general continuous-time zero-coupon market is considered. The problem of optimal portfolios of zero-coupon bonds is…
We adress the maximization problem of expected utility from terminal wealth. The special feature of this paper is that we consider a financial market where the price process of risky assets can have a default time. Using dynamic…
In this paper we derive the exact solution of the multi-period portfolio choice problem for an exponential utility function under return predictability. It is assumed that the asset returns depend on predictable variables and that the joint…