PORTFOLIO OPTIMIZATION UNDER NONLINEAR UTILITY

Robustness-based portfolio optimization under epistemic uncertainty

In this paper, we propose formulations and algorithms for robust portfolio optimization under both aleatory uncertainty (i.e., natural variability) and epistemic uncertainty (i.e., imprecise probabilistic information) arising from interval data. Epistemic uncertainty is represented using two approaches: (1) moment bounding approach and (2) likelihood-based approach. This paper first proposes a ...

Risk and Utility in Portfolio Optimization

Modern portfolio theory(MPT) addresses the problem of determining the optimum allocation of investment resources among a set of candidate assets. In the original mean-variance approach of Markowitz, volatility is taken as a proxy for risk, conflating uncertainty with risk. There have been many subsequent attempts to alleviate that weakness which, typically, combine utility and risk. We present ...

On utility maximization under convex portfolio constraints

Stochastic Portfolio Optimization with Log Utility

A portfolio optimization problem on an infinite time horizon is considered. Risky asset price obeys a logarithmic Brownian motion, and the interest rate varies according to an ergodic Markov diffusion process. Moreover, the interest rate fluctuation is correlated with the risky asset price fluctuation. The goal is to choose optimal investment and consumption policies to maximize the infinite ho...

Utility portfolio optimization with liability and multiple risky assets under the extended CIR model

This paper studies an asset and liability management problem with extended Cox-Ingersoll-Ross (CIR) interest rate, where the financial market is composed of one risk-free asset and multiple risky assets and one zero-coupon bond. We assume that risk-free interest rate is driven by extended CIR interest rate model, while liability is modeled by Brownian motion with drift and is generally correlat...