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Optimal demand for contingent claims when agents have lawinvariant utilities
 Mathematical Finance
, 2011
"... We consider a class of law invariant utilities which contains the Rank Dependent Expected Utility (RDU) and the cumulative prospect theory (CPT). We show that the computation of demand for a contingent claim when utilities are within that class, although not as simple as in the Expected Utility (EU) ..."
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We consider a class of law invariant utilities which contains the Rank Dependent Expected Utility (RDU) and the cumulative prospect theory (CPT). We show that the computation of demand for a contingent claim when utilities are within that class, although not as simple as in the Expected Utility (EU) case, is still tractable. Specific attention is given to the RDU and to the CPT cases. Numerous examples are fully solved. JEL Classification: C0, D8.
Timeinconsistent stochastic linear–quadratic control
 SIAM Journal on Control and Optimization
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Portfolio choice via quantiles
 Mathematical Finance
"... A new portfolio choice model in continuous time is formulated for both complete and incomplete markets, where the quantile function of the terminal cash flow, instead of the cash flow itself, is taken as the decision variable. This formulation covers a wide body of existing and new models with lawi ..."
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Cited by 7 (1 self)
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A new portfolio choice model in continuous time is formulated for both complete and incomplete markets, where the quantile function of the terminal cash flow, instead of the cash flow itself, is taken as the decision variable. This formulation covers a wide body of existing and new models with lawinvariant preference measures, including expected utility maximisation, meanvariance, goal reaching, Yaari’s dual model, Lopes ’ SP/A model, behavioural model under prospect theory, as well as those explicitly involving VaR and CVaR in objectives and/or constraints. A solution scheme to this quantile model is proposed, and then demonstrated by solving analytically the goalreaching model and Yaari’s dual model. A general property derived for the quantile model is that the optimal terminal payment is anticomonotonic with the pricing kernel (or with the minimal pricing kernel in the case of an incomplete market) if the investment opportunity set is deterministic. As a consequence, the mutual fund theorem still holds in a market where rational and irrational agents coexist. Key Words. Portfolio choice, continuous time, quantile function, law invariant measure,
Continuoustime portfolio optimisation for a behavioural investor with bounded utility on gains
 ELECTRONIC COMMUNICATIONS IN PROBABILITY
, 2014
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Nonconvex dynamic programming and optimal investment
, 2015
"... We establish the existence of minimizers in a rather general setting of dynamic stochastic optimization without assuming either convexity or coercivity of the objective function. We apply this to prove the existence of optimal portfolios for nonconcave utility maximization problems in financial mar ..."
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We establish the existence of minimizers in a rather general setting of dynamic stochastic optimization without assuming either convexity or coercivity of the objective function. We apply this to prove the existence of optimal portfolios for nonconcave utility maximization problems in financial market models with frictions, a first result of its kind. The proofs are based on the dynamic programming principle whose validity is established under quite general assumptions.
On optimal investment for a behavioural investor in multiperiod incomplete market models
 IN MATHEMATICAL FINANCE. HTTP://ARXIV.ORG/PDF/1107.1617
, 2013
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Structured portfolio analysis under SharpeOmega
"... This paper deals with performance measurement of
nancial structured products. For this purpose, we introduce the SharpeOmega ratio, based on put as downside risk measure. This allows to take account of the asymmetry of the return probability distribution. We provide general results about the opti ..."
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This paper deals with performance measurement of
nancial structured products. For this purpose, we introduce the SharpeOmega ratio, based on put as downside risk measure. This allows to take account of the asymmetry of the return probability distribution. We provide general results about the optimization of some standard structured portfolios with respect to the SharpeOmega ratio. We determine in particular the optimal combination of risk free, stock and call/put instruments with respect to this performance measure. We show that, contrary to Sharpe ratio maximization (Goetzmann et al., 2002), the payo ¤ of the optimal structured portfolio is not necessarily increasing and concave. We also discuss about the interest of the asset management industry to reward high Sharpe Omega ratios.
Portfolio Choice with Life Annuities under Probability Distortion
"... Retirement planning has attracted considerable attentions from retirees, finance industry and the government. Its significance lies in the protection against individual longevity risk. As a result, optimal portfolio selection problem in a market with annuities has been extensively studied. Yarri (1 ..."
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Retirement planning has attracted considerable attentions from retirees, finance industry and the government. Its significance lies in the protection against individual longevity risk. As a result, optimal portfolio selection problem in a market with annuities has been extensively studied. Yarri (1965) [35] first suggested that individuals with no bequest motive should annuitize all her savings. However, the volume of the voluntary annuity purchases is much lower than predicted by such model, which is the socalled annuity puzzle. In this dissertation, I aim to explore the annuity puzzle from the behavioral economics point of view. Particularly, one major finding from the behavioral experiments is that people always overestimate smallprobability events and underestimate largeprobability events. By introducing the probability distortion on the perceived stock price process, I revisit the dynamic optimal portfolio selection model in a financial market with a riskless bond, a risky asset, and commutable life annuities. In particular, the portfolio problem is studied under both a reverse Sshaped probability distortion function and
Optimal Investment with Transaction Costs under Cumulative Prospect Theory in Discrete Time
"... Abstract We study optimal investment problems under the framework of cumulative prospective theory (CPT). A CPT investor makes investment decisions in a singleperiod financial market with transaction costs. The objective is to seek the optimal investment strategy that maximizes the prospect value ..."
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Abstract We study optimal investment problems under the framework of cumulative prospective theory (CPT). A CPT investor makes investment decisions in a singleperiod financial market with transaction costs. The objective is to seek the optimal investment strategy that maximizes the prospect value of the investor's final wealth. We have obtained the optimal investment strategy explicitly in two examples. An economic analysis is conducted to investigate the impact of the transaction costs and risk aversion on the optimal investment strategy.