The investment industry lacks an unified framework for handling derivative instruments in general portfolio management. With the increased use of derivatives, there is a need for a framework that aligns fundamental terminology and concepts. The main challenges with the current practices are...

This article presents some of the pros and cons of variance and CVaR as portfolio risk measures in mean-risk optimization. While variance is the original risk measure, thoroughly studied for the past 70 years, this article argues that there are practically no reasons for continuing to use...

This essay studies the optimal timing for a firm to adopt a new process innovation in the presence of learning. A policy that has been implemented by governments throughout the world to reduce the cost level of infant industries with positive externalities, is to either subsidize the research of...

This interdisciplinary paper explains how mathematical techniques of stochastic optimal control can be applied to the recent subprime mortgage crisis. Why did the financial markets fail to anticipate the recent debt crisis, despite the large literature in mathematical finance concerning optimal...

In this contribution we propose a dynamic tracking error problem and we consider the problem of monitoring at discrete point the shortfall of the portfolio below a set of given reference levels of wealth. We formulate and solve the resulting dynamic optimization problem using stochastic...

Portfolio optimization literature has come quite far in the decades since the first publication, and many modern models are formulated using second-order cone constraints and take discrete decisions into consideration. In this study, we consider both single-period and multi-period portfolio...

This paper develops an approximate closed-form optimal portfolio allocation formula for a spot asset whose variance follows a GARCH(1,1) process. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected utility from terminal wealth under a...

Dynamic programming is the essential tool in dynamic economic analysis. Problems such as portfolio allocation for individuals and optimal economic growth are typical examples. Numerical methods typically approximate the value function. Recent work has focused on making numerical methods more...

Using a multi-stage stochastic programming method, we suggest an optimal liability-driven investment(LDI) strategy for a closed defined-benefit pension fund including real assets. The objective is to jointly optimize contribution, funding ratio, and buyout cost, subject to a constraint on...

We develop a dynamic programming methodology that seeks to maximize investor outcomes over multiple, potentially competing goals (such as upgrading a home, paying college tuition, or maintaining an income stream in retirement), even when financial resources are limited. Unlike Monte Carlo...