On optimal strategies for utility maximizers in the Arbitrage Pricing Model

We consider a popular model of microeconomics with countably many assets: the Arbitrage Pricing Model. We study the problem of optimal investment under an expected utility criterion and look for conditions ensuring the existence of optimal strategies. Previous results required a certain restrictive hypothesis on the tails of asset return distributions. Using a different method, we manage to remove this hypothesis, at the price of stronger assumptions on the moments of asset returns.Comment: 12 pages, slightly revise

On optimal strategies for utility maximizers in the arbitrage pricing model

We consider a popular model of microeconomics with countably many assets: the Arbitrage Pricing Model. We study the problem of optimal investment under an expected utility criterion and look for conditions ensuring the existence of optimal strategies. Previous results required a certain restrictive hypothesis on the tails of asset return distributions. Using a different method, we manage to remove this hypothesis, at the price of stronger assumptions on the moments of asset returns. © 2016 World Scientific Publishing Company

Evolution of Wealth and Asset Prices in Markets with Case-Based Investors

I analyze whether case-based decision makers (CBDM) can survive in an assetmarket in the presence of expected utilitymaximizers. Conditions are identified, under which the CBDM retain a positive mass with probability one. CBDM can cause predictability of asset returns, high volatility and bubbles. It is found that the expected utility maximizers can disappear from the market for a finite period of time, if the mispricing of the risky asset caused by the case-based decision-makers aggravates too much. Only in the case of logarithmic expected utility maximizers do the case-based decision makers disappear from the market for all parameter values.

The robust superreplication problem: a dynamic approach

In the frictionless discrete time financial market of Bouchard et al.(2015) we consider a trader who, due to regulatory requirements or internal risk management reasons, is required to hedge a claim $\xi$ in a risk-conservative way relative to a family of probability measures $\mathcal{P}$. We first describe the evolution of $\pi_t(\xi)$ - the superhedging price at time $t$ of the liability $\xi$ at maturity $T$ - via a dynamic programming principle and show that $\pi_t(\xi)$ can be seen as a concave envelope of $\pi_{t+1}(\xi)$ evaluated at today's prices. Then we consider an optimal investment problem for a trader who is rolling over her robust superhedge and phrase this as a robust maximisation problem, where the expected utility of inter-temporal consumption is optimised subject to a robust superhedging constraint. This utility maximisation is carrried out under a new family of measures $\mathcal{P}^u$, which no longer have to capture regulatory or institutional risk views but rather represent trader's subjective views on market dynamics. Under suitable assumptions on the trader's utility functions, we show that optimal investment and consumption strategies exist and further specify when, and in what sense, these may be unique

Maximizing expected utility in the Arbitrage Pricing Model

We consider an infinite dimensional optimization problem motivated by mathematical economics. Within the celebrated "Arbitrage Pricing Model", we use probabilistic and functional analytic techniques to show the existence of optimal strategies for investors who maximize their expected utility.Comment: Several corrections, Section 5 adde

Evolution of wealth and asset prices in markets with case-based investors

I analyze whether case-based decision makers (CBDM) can survive in an assetmarket in the presence of expected utilitymaximizers. Conditions are identified, under which the CBDM retain a positive mass with probability one. CBDM can cause predictability of asset returns, high volatility and bubbles. It is found that the expected utility maximizers can disappear from the market for a finite period of time, if the mispricing of the risky asset caused by the case-based decision-makers aggravates too much. Only in the case of logarithmic expected utility maximizers do the case-based decision makers disappear from the market for all parameter values

Optimal Payoffs under State-dependent Preferences

Most decision theories, including expected utility theory, rank dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which income is received. Optimal payoffs have their lowest outcomes when the economy is in a downturn, and this feature is often at odds with the needs of many investors. We introduce a framework for portfolio selection within which state-dependent preferences can be accommodated. Specifically, we assume that investors care about the distribution of final wealth and its interaction with some benchmark. In this context, we are able to characterize optimal payoffs in explicit form. Furthermore, we extend the classical expected utility optimization problem of Merton to the state-dependent situation. Some applications in security design are discussed in detail and we also solve some stochastic extensions of the target probability optimization problem