SSRN Electronic Journal 01/2009; 19(3):487-521. DOI: 10.2139/ssrn.1148724
Source: RePEc

ABSTRACT We develop a Savage-type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries. Our theory permits issue preference; that is, agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues. Hence, we establish subjective foundations for the Anscombe-Aumann framework and other models with two different types of probabilities. We define second-order risk as risk that resolves in the first stage of the compound lottery and show that uncertainty aversion implies aversion to second-order risk which implies issue preference and behavior consistent with the Ellsberg paradox.

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    ABSTRACT: This is a follow up of our previous paper - Trybu{\l}a and Zawisza \cite{TryZaw}, where we considered a modification of a monotone mean-variance functional in continuous time in stochastic factor model. In this article we address the problem of optimizing the mentioned functional in a market with a stochastic interest rate. We formulate it as a stochastic differential game problem and use Hamilton-Jacobi-Bellman-Isaacs equations to derive the optimal investment strategy and the value function.
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    ABSTRACT: In a mean variance framework, we analyse risk taking in the presence of a (possibly) dependent background risk, exemplified in a linear portfolio selection problem. We first characterise the comparative statics of changes in the distribution and dependence structure of the background risk. For unfair, undesirable and loss-aggravating increases in background risks (both dependent and independent), we then present necessary and sufficient restrictions on preferences such that greater background uncertainty leads to reduced risk taking. With mean-variance preferences, these restrictions boil down to simple conditions on the marginal rate of substitution between risk and return. They can be easily related to familiar notions such as risk vulnerability, properness or standardness.
    Journal of Mathematical Economics 12/2012; 48(6). DOI:10.1016/j.jmateco.2012.09.001 · 0.50 Impact Factor
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    ABSTRACT: This paper presents an agent-based model to select an investment portfolio with a restriction on the number of stocks in it. Daily movements of all the stocks in the market for the past few years are assumed to be available. The scheme deploys a federally structured consortium of agents in the stock market at the start of the historical period. Each agent starts with a pseudorandom portfolio and follows individual investment strategies as it walks through the past data. The agents are designed to emulate some of the characteristics of human investors-adjusting the weights of the stocks based on its own attitude toward risk, occasionally dropping and adding stocks to the portfolio, etc. Periodically, the agents share information about their performances and can switch portfolios. A final cardinality constrained portfolio is constructed by consolidating individual portfolios arrived at by the agents working on the historical data of the stocks. When tested in real markets of the U.K. and Japan, the model suggested portfolios that were quite competitive to, and frequently better than, the portfolios suggested by the mean-variance models.
    IEEE Transactions on Systems Man and Cybernetics Part C (Applications and Reviews) 11/2012; 42(6):1510-1518. DOI:10.1109/TSMCC.2012.2197388 · 1.53 Impact Factor

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