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This paper is concerned with the axiomatic foundation and explicit construction of a general class of optimality criteria that can be used for investment problems with multiple time horizons, or when the time horizon is not known in…
We investigate the portfolio execution problem under a framework in which volatility and liquidity are both uncertain. In our model, we assume that a multidimensional Markovian stochastic factor drives both of them. Moreover, we model…
We consider a robust switching control problem. The controller only observes the evolution of the state process, and thus uses feedback (closed-loop) switching strategies, a non standard class of switching controls introduced in this paper.…
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 derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio…
This paper investigates a robust optimal consumption, investment, and reinsurance problem for an insurer with Epstein-Zin recursive preferences operating under model uncertainty. The insurer's surplus follows the diffusion approximation of…
We revisit Markowitz's mean-variance portfolio selection model by considering a distributionally robust version, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures…
We introduce an infinite-horizon, continuous-time portfolio selection problem faced by an agent with periodic S-shaped preference and present bias. The inclusion of a quasi-hyperbolic discount function leads to time-inconsistency and we…
This paper concerns a continuous time mean-variance (MV) portfolio selection problem in a jump-diffusion financial model with no-shorting trading constraint. The problem is reduced to two subproblems: solving a stochastic linear-quadratic…
This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the timeinconsistent stopping control problems under…
In this paper, we consider a continuous-time mean-variance portfolio selection with regime-switching and random horizon. Unlike previous works, the dynamic of assets are described by non-Markovian regime-switching models in the sense that…
This paper considers the mean-reverting portfolio design problem arising from statistical arbitrage in the financial markets. We first propose a general problem formulation aimed at finding a portfolio of underlying component assets by…
This paper studies dynamic asset allocation with interest rate risk and several sources of ambiguity. The market consists of a risk-free asset, a zero-coupon bond (both determined by a Vasicek model), and a stock. There is ambiguity about…
We consider the problem of optimizing a portfolio of financial assets, where the number of assets can be much larger than the number of observations. The optimal portfolio weights require estimating the inverse covariance matrix of excess…
The monotone mean-variance (MMV) preference proposed by Maccheroni, et al. (Math. Finance 19(3): 487-521, 2009) fails to differentiate strictly dominant payoffs, which may cause inconsistency in portfolio decision-making. This paper…
The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…
We study continuous-time mean--variance portfolio selection in markets where stock prices are diffusion processes driven by observable factors that are also diffusion processes, yet the coefficients of these processes are unknown. Based on…
We provide a unified approach to find equilibrium solutions for time-inconsistent problems with distribution dependent rewards, which are important to the study of behavioral finance and economics. Our approach is based on {\it equilibrium…
We propose to solve large scale Markowitz mean-variance (MV) portfolio allocation problem using reinforcement learning (RL). By adopting the recently developed continuous-time exploratory control framework, we formulate the exploratory MV…
We consider a stock that follows a geometric Brownian motion (GBM) and a riskless asset continuously compounded at a constant rate. We assume that the stock can go bankrupt, i.e., lose all of its value, at some exogenous random time…