We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small transaction costs is used to obtain a tractable model. A...

This survey is an introduction to asymptotic methods for portfolio-choice problems with small transaction costs. We outline how to derive the corresponding dynamic programming equations and simplify them in the small-cost limit. This allows to obtain explicit solutions in a wide range of...

We solve the problem of optimal risk management for an investor holding an illiquid, alpha generating fund and hedging his position with a liquid futures contract. When the investor is subject to a drawdown constraint, he is forced to reduce the total risk of his portfolio after a drawdown. In...

We solve the problem of optimal inventory management for a CARA market-maker who faces proportional transaction costs and marking to market. Our model accommodates inventory shocks following an arbitrary compound Poisson process, and allows us to link the optimal policy to the moment-generating...

Despite clear evidence of correlations between financial and medical statuses and decisions, most models treat financial and health-related choices separately. This paper bridges this gap by proposing a tractable dynamic framework for the joint determination of optimal consumption, portfolio...

This chapter surveys theoretical research on the long-term performance of fixed-mix investment strategies. These self-financing strategies rebalance the portfolio over time so as to keep constant the proportions of wealth invested in various assets. The main result is that wealth can be grown...

We develop alternative models for hedging yield curve risk and test them by hedging US Treasury bond portfolios through note/bond futures. We show that traditional implementations of models based on principal component analysis, duration vectors and key rate duration lead to high exposure to...

Reference-dependent preference models assume that agents derive utility from deviations of consumption from benchmark levels, rather than from consumption levels. These references can be either backward-looking (as explicit in the Habit literature) or forward-looking (as implicitly suggested by...

Following Levy and Roll [2010], we posit that the market portfolio is the efficient tangent Markowitz portfolio, i.e., it is mean-variance efficient. We then reverse engineer the expected returns and variance terms with constraints imposed by empirical data on a hierarchy of asset baskets. This...