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on Utility Models and Prospect Theory |
| By: | Chenghu Ma; Wing-Keung Wong |
| Abstract: | Is it possible to obtain an objective and quantifiable measure of risk backed up by choices made by some specific groups of rational investors? To answer this question, in this paper we establish some behavior foundations for various types of VaR models, including VaR and conditional-VaR, as measures of downside risk. Though supported to some extent with unanimous choices by some specific groups of expected or non-expected utility investors, VaRs as profiles of risk measures at various levels of risk tolerance are not quantifiable – they can only provide partial and incomplete risk assessments for risky prospects. Also included in our discussion are the relevant VaRs and several alternative risk measures for investors; these alternatives use somewhat weaker assumptions about risk-averse behavior by incorporating a mean-preserving-spread. For this latter group of investors, we provide arguments for and against the standard deviation vs. VaR and conditional VaRs as objective and quantifiable measures of risk in the context of portfolio choice. |
| Keywords: | downside risk, value-at-risk, conditional-VaR, stochastic dominance, utility |
| JEL: | C0 D81 G10 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:001971&r=upt |
| By: | Wing-Keung Wong; Chenghu Ma |
| Abstract: | This paper extends the work on location-scale (LS) family with general n random seed sources. First, we clarify and generalize existing results in this multivariate setting. Some useful geometrical and topological properties of the location-scale expected utility functions are obtained. Second, we introduce and study some general non-expected utility functions defined over the LS family. Special care is taken in characterizing the shapes of the indifference curves induced by the location-scale expected utility functions and non-expected utility functions. Finally, efforts are also made to study several well-defined partial orders and dominance relations defined over the LS family. These include the first- and second-order stochastic dominances, the mean-variance rule, and a newly defined location-scale dominance. |
| Keywords: | Location-scale family,Inverse problem,Non-expected utility function, Stochastic dominance, Location-scale dominance, Mean-variance rule |
| JEL: | G11 C60 G10 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002086&r=upt |
| By: | Éric André |
| Abstract: | Axiomatic models of decision under ambiguity with a non-unique prior allow for the existence of Crisp Fair Gambles: acts whose expected utility is nul whichever of the priors is used. But, in these models, the DM has to be indifferent to the addition of such acts. Their existence is then at odds with a preference taking into account the variance of the prospects. In this paper we study some geometrical and topological properties of the set of priors that would rule out the existence of Crisp Fair Gambles, properties which have consequences on what can be an unambiguous financial asset. |
| Keywords: | monotone mean-variance preferences, Ambiguity, set of priors, crisp acts, unambiguous asset |
| JEL: | D81 G11 |
| Date: | 2014–03–25 |
| URL: | http://d.repec.org/n?u=RePEc:aim:wpaimx:1410&r=upt |
| By: | Chenghu Ma; Jiankang Zhang |
| Abstract: | This paper tackles the "aggregation problem" for stochastic economies with possibly incomplete market. An "aggregation theorem" is proved towards an analytic construction of the representative agent’s utility function. This is done within a general time-state setup with general utility functions and without restrictions on the initial resource allocations. Welfare implications, concerning the social welfare loss resulting from market incompleteness, are readily reflected from the constructed representative agent’s utility function |
| Keywords: | Aggregation, constrained Pareto optimal, incomplete market |
| JEL: | D52 G11 G12 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002004&r=upt |
| By: | Ole Peters; Murray Gell-Mann |
| Abstract: | The classic decision-theory problem of evaluating a gamble is treated from a modern perspective using dynamics. Linear and logarithmic utility functions appear not as expressions for the value of money but as mappings that result in ergodic observables for purely additive and purely multiplicative dynamics, the most natural stochastic processes to model wealth. This perspective is at odds with the boundedness requirement for utility functions in the dominant formalism of decision theory. We highlight conceptual and mathematical inconsistencies throughout the development of decision theory, whose correction clarifies that the modern perspective is legitimate and that boundedness of utility functions is not required. |
| Date: | 2014–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1405.0585&r=upt |
| By: | Qian Han |
| Abstract: | Considering a production economy with an arbitrary von-Neumann Morgenstern utility, this paper derives a general equilibrium relationship between the market prices of risks and market risk aversion under a continuous time stochastic volatility model completed by liquidly traded options. The derived relation shows that in equilibrium the risk aversion should be a linear combination of the market price of asset risk and market price of orthogonal risk. Construction of a daily market risk aversion index is proposed to help practitioners with better risk management. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002033&r=upt |
| By: | Zuo Quan Xu; Fahuai Yi |
| Abstract: | A continuous-time consumption-investment model with constraint is considered for a small investor whose decisions are the consumption rate and the allocation of wealth to a risk-free and a risky asset with logarithmic Brownian motion fluctuations. The consumption rate is subject to an upper bound constraint which linearly depends on the investor's wealth and bankruptcy is prohibited. The investor's objective is to maximize total expected discounted utility of consumption over an infinite trading horizon. It is shown that the value function is (second order) smooth everywhere but a unique possibility of (known) exception point and the optimal consumption-investment strategy is provided in a closed feedback form of wealth, which in contrast to the existing work does not involve the value function. According to this model, an investor should take the same optimal investment strategy as in Merton's model regardless his financial situation. By contrast, the optimal consumption strategy does depend on the investor's financial situation: he should use a similar consumption strategy as in Merton's model when he is in a bad situation, and consume as much as possible when he is in a good situation. |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1404.7698&r=upt |
| By: | Chenghu Ma |
| Abstract: | This paper studies sequential portfolio choices by MPS-risk-averse investors in a continuous time jump-diffusion framework. It is shown that the optimal trading strategies for MPS risk averse investors, if they exist, must be located on a so-called ‘temporal efficient frontier’ (t.e.f.). Analytic and qualitative characterizations of the t.e.f. are provided and are shown to form a hyperbola in the μ-σ plane. This paper also provides insights on (i) dynamic consistency underlying those temporal efficient trading strategies; (ii) mutual fund separation in extending the classical notion of Tobin (1958) and Black (1972) to this continuous-time setting; (iii) risk decomposition in presence of Lévy jumps, and (iv) differences between MPS risk averse investors |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:001977&r=upt |
| By: | Chenghu Ma |
| Abstract: | This paper is to provide a theoretical foundation of incomplete contract in an extensive game of multi-agent interaction. It aims to explain why rational agents may agree upon incomplete contracts even though it is costless to sign a complete one. It is argued that an incomplete contract creates strategic uncertainty. If agents’ attitudes toward uncertainty are not neutral, then an incomplete contract as final solution can be the consequence of common knowledge of rationality. This paper assumes that all agents are uncertainty averse in a sense of Gilboa and Schmeidler (1989); and that agents can form coalitions as part of strategic play. All these are embedded into a newly proposed equilibrium solution concept for extensive form game of perfect information. |
| Keywords: | uncertainty aversion, strategic uncertainty, coalitionformation, stability and core-criterion. |
| JEL: | C70 C71 C72 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:001970&r=upt |
| By: | Chenghu Ma |
| Abstract: | This paper derives an equilibrium formula for pricing European options and other contingent claims which allows incorporating impacts of several important economic variable on security prices including, among others, representative agent preferences, future volatility and rare jump events. The derived formulae is general and flexible enough to include some important option pricing formulae in the literature, such as Black-Scholes, Naik-Lee, Cox-Ross and Merton option pricing formulae. The existence of jump risk as a potential explanation of the moneyness biases associated with the Black-Scholes model is explored. |
| Keywords: | equilibrium option pricing, recursive utility, Levy jumps. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:001995&r=upt |
| By: | Phelim P. Boyle; Chenghu Ma |
| Abstract: | This paper establishes conditions under which the classical CAPM holds in equilibrium. Our derivation uses simple arguments to clarify and extend results available in the literature. We show that if agents are risk averse in the sense of mean-preserving-spread (MPS) the CAPM will necessarily hold, along with two-fund separation. We derive this result without imposing any distributional assumptions on asset returns. The CAPM holds even when the market contains an infinite number of securities and when investors only hold finite portfolios. Our paper complements the results of Duffie(1988) who provided an abstract derivation of the CAPM under some somewhat more technical assumptions. In addition we use simple arguments to prove the existence of equilibrium with MPS-risk-averse investors without assuming that the market is complete. Our proof does not require any additional restrictions on the asset returns, except that the co-variance matrix for the returns on the risky securities is non-singular. |
| Keywords: | CAPM equilibrium, two-fund separation, generalized efficient portfolio, MPS-risk-aversion. JEL |
| JEL: | D50 D81 G10 G11 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:001969&r=upt |