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In this note, we explicitly solve the problem of maximizing utility of consumption (until the minimum of bankruptcy and the time of death) with a constraint on the probability of lifetime ruin, which can be interpreted as a risk measure on…
We consider an investor who wants to select her/his optimal consumption, investment and insurance policies. Motivated by new insurance products, we allow not only the financial marke but also the insurable loss to depend on the regime of…
We address the Merton problem of maximizing the expected utility of terminal wealth using techniques from variational analysis. Under a general continuous semimartingale market model with stochastic parameters, we obtain a characterization…
Portfolio selection problems that optimize expected utility are usually difficult to solve. If the number of assets in the portfolio is large, such expected utility maximization problems become even harder to solve numerically. Therefore,…
In this paper, we work in the framework of the Merton problem but we impose a drawdown constraint on the consumption process. This means that consumption can never fall below a fixed proportion of the running maximum of past consumption. In…
This paper studies a life-cycle optimal portfolio-consumption problem when the consumption performance is measured by a shortfall aversion preference with an additional drawdown constraint on consumption rate. Meanwhile, the agent also…
In this paper, we propose a new class of optimization problems, which maximize the terminal wealth and accumulated consumption utility subject to a mean variance criterion controlling the final risk of the portfolio. The multiple-objective…
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,…
This paper studies a type of periodic utility maximization for portfolio management in an incomplete market model, where the underlying price diffusion process depends on some external stochastic factors. The portfolio performance is…
This work initiates research into the problem of determining an optimal investment strategy for investors with different attitudes towards the trade-offs of risk and profit. The probability distribution of the return values of the stocks…
This paper studies an optimal investing problem for a retiree facing longevity risk and living standard risk. We formulate the investing problem as a portfolio choice problem under a time-varying risk capacity constraint. We derive the…
We study a portfolio optimization problem for competitive agents with CRRA utilities and a common finite time horizon. The utility of an agent depends not only on her absolute wealth and consumption but also on her relative wealth and…
We examine the problem of optimal portfolio allocation within the framework of utility theory. We apply exponential utility to derive the optimal diversification strategy and logarithmic utility to determine the optimal leverage. We enhance…
We consider a variation on the classical finance problem of optimal portfolio design. In our setting, a large population of consumers is drawn from some distribution over risk tolerances, and each consumer must be assigned to a portfolio of…
This paper investigates Merton's portfolio problem in a rough stochastic environment described by Volterra Heston model. The model has a non-Markovian and non-semimartingale structure. By considering an auxiliary random process, we solve…
In this paper, we study an intertemporal utility maximization problem in which an investor chooses consumption and portfolio strategies in the presence of a stochastic factor and a no-borrowing constraint. In the spirit of the Kim-Omberg…
The paper [12] examines a concept of equilibrium policies instead of optimal controls in stochastic optimization to analyze a mean-variance portfolio selection problem. We follow the same approach in order to investigate the Merton…
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…
The aim of this short note is to establish a limit theorem for the optimal trading strategies in the setup of the utility maximization problem with proportional transaction costs. This limit theorem resolves the open question from [4]. The…
This paper concerns the numerical solution of a fully nonlinear parabolic double obstacle problem arising from a finite portfolio selection with proportional transaction costs. We consider the optimal allocation of wealth among multiple…