Jianming Xia

Arrow-Debreu Equilibria for Rank-Dependent Utilities

We provide conditions on a one-period-two-date pure exchange economy with rank-dependent utility agents under which Arrow-Debreu equilibria exist. When such an equilibrium exists, we derive the state-price density explicitly, which is a weighted marginal rate of substitution between the initial and the end-of-period consumption of a representative agent, while the weight is expressed through the differential of the probability weighting function. Based on the result we reach several findings, including that asset prices depend upon agents’ subjective beliefs regarding overall consumption growth, that an uncorrelated security’s entire probability distribution and its interdependence with the other part of the economy should be priced, and that there is a direction of thinking about the equity premium and risk-free rate puzzles.

Multi-agent investment in incomplete markets

Abstract.The problem of the expected utility maximization in incomplete markets for a single agent is well understood in a fairly general setting. This paper studies the problem for the multi-agent case. For this case a cooperative investment game is posed as follows: firstly collect all agents’ capital together at the initial time, then invest the total capital in a trading strategy, and finally divide the terminal wealth of the trading strategy and each of them gets a part. We give a characterization of Pareto optimal cooperative strategies and a characterization of situations where cooperation strictly Pareto dominates non cooperation, and prove that the core of the cooperative investment game is non-empty under mild conditions using Scarf theorem.

Risk Aversion and Portfolio Selection in a Continuous-Time Model

The comparative statics of the optimal portfolios across individuals is carried out for the Black-Scholes market model. It turns out that the indirect utility functions inherit the order of risk aversion (in the Arrow-Pratt sense) from the von Neumann-Morgenstern utility functions, and therefore, a more risk-averse agent would invest less wealth (in absolute value) in the risky asset.

Some Remarks on Arbitrage Pricing Theory

AbstractIn this note we report main results in a recent paper by the authors, in which we established a version of Kramkovs optional decomposition theorem in the setting of equivalent martingale measures and using this theorem we clarified some basic concepts and results in arbitrage pricing theory: superhedging, fair price, replicatable contingent claim, complete markets.

Cooperative hedging in incomplete markets

Abstract The problem of (partial) hedging contingent claims for a single agent is well studied. This paper studies the problem for the multiagent case in incomplete markets. For this case, a cooperative hedging game is posed as follows: First, all agents contribute some money and collect the money together as the initial total capital, then invest the initial total capital in a trading strategy, and, finally, divide the terminal wealth of the trading strategy and each of them gets a part. We give a characterization of the optimal cooperative hedging strategy and prove that the core of the cooperative hedging game, as a cooperative game with side payment, is nonempty.

Dividing gains between a client and her agent

Abstract. A client(she) contracts with an agent(him), who has limited liability, as follows: she lends him one dollar at time 0 and he uses the money to trade in a security market. As return, he promises to give her a fixed amount

Optimal investment for an insurer: The martingale approach

e^{r_0T}

MARKOWITZ'S PORTFOLIO OPTIMIZATION IN AN INCOMPLETE MARKET

at the final time T; in addition, if the real return rate of the strategy is larger than

Mean-Variance Portfolio Choice: Quadratic Partial Hedging

r_0

A new look at some basic concepts in arbitrage pricing theory

, she can also get a fixed proportion