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We study the problem of maximising terminal utility for an agent facing model uncertainty, in a frictionless discrete-time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the…
We study the continuous time portfolio optimization model on the market where the mean returns of individual securities or asset categories are linearly dependent on underlying economic factors. We introduce the functional $Q_\gamma$…
We consider the value function of a stochastic optimal control of degenerate diffusion processes in a domain $D$. We study the smoothness of the value function, under the assumption of the non-degeneracy of the diffusion term along the…
In hedge funds, convex compensation schemes are adopted to stimulate a high-profit performance for portfolio managers. In economics, non-monotone risk aversion is proposed to argue that individuals may not be risk-averse when the wealth…
This paper addresses the problem of utility maximization under uncertain parameters. In contrast with the classical approach, where the parameters of the model evolve freely within a given range, we constrain them via a penalty function. We…
We investigate optimal consumption policies in the liquidity risk model introduced in Pham and Tankov (2007). Our main result is to derive smoothness results for the value functions of the portfolio/consumption choice problem. As an…
Stock portfolio optimization is the process of continuous reallocation of funds to a selection of stocks. This is a particularly well-suited problem for reinforcement learning, as daily rewards are compounding and objective functions may…
In this paper, we explore the portfolio allocation problem involving an uncertain covariance matrix. We calculate the expected value of the Constant Absolute Risk Aversion (CARA) utility function, marginalized over a distribution of…
We study the worst portfolios for a class of law invariant dynamic monetary utility functions with domain in a class of stochastic processes. The concept of comonotonicity is introduced for these processes in order to prove the existence of…
We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving…
In this paper, we consider $n$ agents who invest in a general financial market that is free of arbitrage and complete. The aim of each investor is to maximize her expected utility while ensuring, with a specified probability, that her…
We study the optimal investment problem for a homogeneous collective of $n$ individuals investing in a Black-Scholes model subject to longevity risk with Epstein--Zin preferences. %and with preferences given by power utility. We compute…
We consider a trader who wants to direct his portfolio towards a set of acceptable wealths given by a convex risk measure. We propose a black-box algorithm, whose inputs are the joint law of stock prices and the convex risk measure, and…
This article focuses on a class of distributionally robust optimization (DRO) problems where, unlike the growing body of the literature, the objective function is potentially nonlinear in the distribution. Existing methods to optimize…
The comparative statics of the optimal portfolios across individuals is carried out for a continuous-time complete market model, where the risky assets price process follows a joint geometric Brownian motion with time-dependent and…
In this paper, we consider the problem of maximizing the expected discounted utility of dividend payments for an insurance company that controls risk exposure by purchasing proportional reinsurance. We assume the preference of the insurer…
The main purpose of this paper is to analyze solutions to a fully nonlinear parabolic equation arising from the problem of optimal portfolio construction. We show how the problem of optimal stock to bond proportion in the management of…
We propose a novel portfolio selection approach that manages to ease some of the problems that characterise standard expected utility maximisation. The optimal portfolio is no longer defined as the extremum of a suitably chosen utility…
In an arbitrage-free simple market, we demonstrate that for a class of state-dependent exponential utilities, there exists a unique prediction of the random risk aversion that ensures the consistency of optimal strategies across any time…
The risk of financial positions is measured by the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability constraint. We investigate nondegeneracy, finiteness and…