Related papers: Continuous-Time Markowitz's Model with Transaction…

The focal point of this paper is the issue of "drawdown" which arises in recursive betting scenarios and related applications in the stock market. Roughly speaking, drawdown is understood to mean drops in wealth over time from peaks to…

In this paper, we study a free boundary problem, which arises from an optimal trading problem of a stock that is driven by a uncertain market status process. The free boundary problem is a variational inequality system of three functions…

This paper considers the constrained portfolio optimization in a generalized life-cycle model. The individual with a stochastic income manages a portfolio consisting of stocks, a bond, and life insurance to maximize his or her consumption…

The signal-noise ratio of a portfolio of p assets, its expected return divided by its risk, is couched as an estimation problem on the sphere. When the portfolio is built using noisy data, the expected value of the signal-noise ratio is…

This paper considers the optimal control of time varying continuous time Markov chains whose transition rates are themselves Markov processes. In one set of problems the solution of an ordinary differential equation is shown to determine…

We propose a continuous time model for financial markets with proportional transactions costs and a continuum of risky assets. This is motivated by bond markets in which the continuum of assets corresponds to the continuum of possible…

Portfolio optimization has long been dominated by covariance-based strategies, such as the Markowitz Mean-Variance framework. However, these approaches often fail to ensure a balanced risk structure across assets, leading to concentration…

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…

Designing an optimum portfolio for allocating suitable weights to its constituent assets so that the return and risk associated with the portfolio are optimized is a computationally hard problem. The seminal work of Markowitz that attempted…

We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…

This paper considers an optimal control problem for a linear mean-field stochastic differential equation having regime switching with quadratic functional in the large time horizons. Our main contribution lies in establishing the strong…

We study shortfall risk minimization for American options with path dependent payoffs under proportional transaction costs in the Black--Scholes (BS) model. We show that for this case the shortfall risk is a limit of similar terms in an…

In this paper, we study a continuous-time discounted jump Markov decision process with both controlled actions and observations. The observation is only available for a discrete set of time instances. At each time of observation, one has to…

Trailing stop is a popular stop-loss trading strategy by which the investor will sell the asset once its price experiences a pre-specified percentage drawdown. In this paper, we study the problem of timing buy and then sell an asset subject…

We consider how to optimally allocate investments in a portfolio of competing technologies using the standard mean-variance framework of portfolio theory. We assume that technologies follow the empirically observed relationship known as…

The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual…

Volatility, as a primary indicator of financial risk, forms the foundation of classical frameworks such as Markowitz's Portfolio Theory and the Efficient Market Hypothesis (EMH). However, its conventional use rests on assumptions-most…

This paper examines the retirement decision, optimal investment, and consumption strategies under an age-dependent force of mortality. We formulate the optimization problem as a combined stochastic control and optimal stopping problem with…

In finance industry portfolio construction deals with how to divide the investors' wealth across an asset-classes' menu in order to maximize the investors' gain. Main approaches in use at the present are based on variations of the classical…

The subject of this paper is an optimal consumption/optimal portfolio problem with transaction costs and with multiple risky assets. In our model the transaction costs take a special form in that transaction costs on purchases of one of the…