Related papers: Merton's Problem with Recursive Perturbed Utility
We study the problem of optimal portfolio selection under stochastic volatility within a continuous time reinforcement learning framework with portfolio constraints. Exploration is modeled through entropy-regularized relaxed controls, where…
In the frictionless discrete time financial market of Bouchard et al.(2015) we consider a trader who, due to regulatory requirements or internal risk management reasons, is required to hedge a claim $\xi$ in a risk-conservative way relative…
This study investigates an optimal consumption--investment problem in which the unobserved stock trend is modulated by a hidden Markov chain that represents different economic regimes. In the classical approach, the hidden state is…
This paper studies the properties of discrete time stochastic optimal control problems associated with portfolio selection. We investigate if optimal continuous time strategies can be used effectively for a discrete time market after a…
Portfolio selection in the periodic investment of securities modeled by a multivariate Merton model with dependent jumps is considered. The optimization framework is designed to maximize expected terminal wealth when portfolio risk is…
Monotone mean-variance (MMV) utility is the minimal modification of the classical Markowitz utility that respects rational ordering of investment opportunities. This paper provides, for the first time, a complete characterization of optimal…
This paper investigates the use of risk measures and theories of choice for modeling risk-averse route choice and traffic network equilibrium with random travel times. We interpret the postulates of these theories in the context of routing,…
The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a…
We study consumption dependence in the context of random utility and repeated choice. We show that, in the presence of consumption dependence, the random utility model is a misspecified model of repeated rational choice. This…
In this paper, we consider a dynamic coalition portfolio selection problem, with each agent's objective given by an Epstein--Zin recursive utility. To find a Pareto optimum, the coalition's problem is formulated as an optimization problem…
In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under…
Acquisition of data is a difficult task in many applications of machine learning, and it is only natural that one hopes and expects the population risk to decrease (better performance) monotonically with increasing data points. It turns…
The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models…
We study a general robust utility maximization problem in a discrete-time frictionless market. The investor is assumed to have a possibly infinite, random, nonconcave, and nondecreasing utility function defined on the whole real line. She…
In this paper we study a robust expected utility maximization problem with random endowment in discrete time. We give conditions under which an optimal strategy exists and derive a dual representation for the optimal utility. Our approach…
We revisit Merton's portfolio optimization problem under boun-ded state-dependent utility functions, in a market driven by a L\'evy process $Z$ extending results by Karatzas et. al. (1991) and Kunita (2003). The problem is solved using a…
This paper studies a robust portfolio optimization problem under the multi-factor volatility model introduced by Christoffersen et al. (2009). The optimal strategy is derived analytically under the worst-case scenario with or without…
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…
We study a portfolio selection problem in a continuous-time It\^o-Markov additive market with prices of financial assets described by Markov additive processes which combine L\'evy processes and regime switching models. Thus the model takes…
We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for…