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28
Behavioral portfolio selection in continuous time
 Mathematical Finance
, 2008
"... This paper formulates and studies a general continuoustime behavioral portfolio selection model under Kahneman and Tversky’s (cumulative) prospect theory, featuring Sshaped utility (value) functions and probability distortions. Unlike the conventional expected utility maximization model, such a be ..."
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This paper formulates and studies a general continuoustime behavioral portfolio selection model under Kahneman and Tversky’s (cumulative) prospect theory, featuring Sshaped utility (value) functions and probability distortions. Unlike the conventional expected utility maximization model, such a behavioral model could be easily misformulated (a.k.a. illposed) if its different components do not coordinate well with each other. Certain classes of an illposed model are identified. A systematic approach, which is fundamentally different from the ones employed for the utility model, is developed to solve a wellposed model, assuming a complete market and general Itô processes for asset prices. The optimal terminal wealth positions, derived in fairly explicit forms, possess surprisingly simple structure reminiscent of a gambling policy betting on a good state of the world while accepting a fixed, known loss in case of a bad one. An example with a twopiece CRRA utility is presented to illustrate the general results obtained, and is solved completely for all admissible parameters. The effect of the behavioral criterion on the risky allocations is finally discussed.
Mean–variance optimal adaptive execution
 Applied Mathematical Finance
, 2011
"... Electronic trading of equities and other securities makes heavy use of “arrival price ” algorithms, that balance the market impact cost of rapid execution against the volatility risk of slow execution. In the standard formulation, meanvariance optimal trading strategies are static: they do not modi ..."
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Cited by 11 (1 self)
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Electronic trading of equities and other securities makes heavy use of “arrival price ” algorithms, that balance the market impact cost of rapid execution against the volatility risk of slow execution. In the standard formulation, meanvariance optimal trading strategies are static: they do not modify the execution speed in response to price motions observed during trading. We show that substantial improvement is possible by using dynamic trading strategies, and that the improvement is larger for large initial positions. We develop a technique for computing optimal dynamic strategies to any desired degree of precision. The asset price process is observed on a discrete tree with a arbitrary number of levels. We introduce a novel dynamic programming technique in which the control variables are not only the shares traded at each time step, but also the maximum expected cost for the remainder of the program; the value function is the variance of the remaining program. The resulting adaptive strategies are “aggressiveinthemoney”: they accelerate the execution when the price moves in the trader’s favor, spending parts of the trading gains to reduce risk.
Comparison between the mean variance optimal and the mean quadratic variation optimal trading strategies.
, 2011
"... Abstract We compare optimal liquidation policies in continuous time in the presence of trading impact using numerical solutions of Hamilton Jacobi Bellman (HJB) partial differential equations (PDE). In particular, we compare the path dependent, timeconsistent meanquadraticvariation strategy with ..."
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Abstract We compare optimal liquidation policies in continuous time in the presence of trading impact using numerical solutions of Hamilton Jacobi Bellman (HJB) partial differential equations (PDE). In particular, we compare the path dependent, timeconsistent meanquadraticvariation strategy with the pathindependent, timeinconsistent (precommitment) meanvariance strategy. We show that the two different risk measures lead to very different strategies and liquidation profiles. In terms of the optimal trading velocities, the meanquadraticvariation strategy is much less sensitive to changes in asset price and varies more smoothly. In terms of the liquidation profiles, the meanvariance strategy strategy is much more variable, although the mean liquidation profiles for the two strategies are surprisingly similar. On a numerical note, we show that using an interpolation scheme along a parametric curve in conjunction with the semiLagrangian method results in significantly better accuracy than standard axisaligned linear interpolation. We also demonstrate how a scaled computational grid can improve solution accuracy.
2009) “Implications of the Sharpe Ratio as a Performance Measure in MultiPeriod Settings
 Journal of Economic Dynamics and Control
"... We study effects of using Sharpe ratio as a performance measure for compensating money managers in a dynamic and frictionless market setting. First, we demonstrate that with such a performance measure, the manager’s focus on the short horizon performance is detrimental to the investor’s long horizon ..."
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We study effects of using Sharpe ratio as a performance measure for compensating money managers in a dynamic and frictionless market setting. First, we demonstrate that with such a performance measure, the manager’s focus on the short horizon performance is detrimental to the investor’s long horizon performance. Numerical experiments illustrate that when returns are iid, the performance loss is significant, even when the investor’s investment horizon is not much longer than the manager’s. When expected returns are mean reverting, the performance loss is exacerbated. Second, we show that Sharpe ratio maximization strategies tend to increase (decrease) the risk in the later part of the optimization period after a bad (good) performance in the earlier part of the optimization period. As illustrated by a simulation exercise, this prediction is in agreement with empirical observations, and it presents a rational expectations
On Efficiency of MeanVariance based Portfolio Selection in DC Pension Schemes. Collegio Carlo Alberto
, 2010
"... www.carloalberto.org/working_papers © 2010 by Elena Vigna. Any opinions expressed here are those of the authors and not those of theCollegio Carlo Alberto. On efficiency of meanvariance based portfolio selection in DC pension schemes ..."
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www.carloalberto.org/working_papers © 2010 by Elena Vigna. Any opinions expressed here are those of the authors and not those of theCollegio Carlo Alberto. On efficiency of meanvariance based portfolio selection in DC pension schemes
A Convex Stochastic Optimization Problem Arising from Portfolio Selection
 Mathematical Finance
, 2008
"... A continuoustime financial portfolio selection model with expected utility maximization typically boils down to solving a (static) convex stochastic optimization problem in terms of the terminal wealth, with a budget constraint. In literature the latter is solved by assuming a priori that the probl ..."
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Cited by 3 (1 self)
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A continuoustime financial portfolio selection model with expected utility maximization typically boils down to solving a (static) convex stochastic optimization problem in terms of the terminal wealth, with a budget constraint. In literature the latter is solved by assuming a priori that the problem is wellposed (i.e., the supremum value is finite) and a Lagrange multiplier exists (and as a consequence the optimal solution is attainable). In this paper it is first shown, via various counterexamples, neither of these two assumptions needs to hold, and an optimal solution does not necessarily exist. These anomalies in turn have important interpretations in and impacts on the portfolio selection modeling and solutions. Relations among the nonexistence of the Lagrange multiplier, the illposedness of the problem, and the nonattainability of an optimal solution are then investigated. Finally, explicit and easily verifiable conditions are derived which lead to finding the unique optimal solution. Key words: portfolio selection, convex stochastic optimization, Lagrange multiplier, wellposedness, attainability 1
Pricing and Hedging of Credit Risk: Replication and MeanVariance Approaches
 CONTEMPORARY MATHEMATICS
"... The paper presents some methods and results related to the valuation and hedging of defaultable claims (creditrisk sensitive derivative instruments). Both the exact replication of attainable defaultable claims and the meanvariance hedging of nonattainable defaultable claims are examined. For th ..."
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The paper presents some methods and results related to the valuation and hedging of defaultable claims (creditrisk sensitive derivative instruments). Both the exact replication of attainable defaultable claims and the meanvariance hedging of nonattainable defaultable claims are examined. For the sake of simplicity, the general methods are then applied to simple cases of defaultable equity derivatives, rather than to the more complicated examples of reallife credit derivatives.
Meanvariance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes,” CeRP Working Papers
, 2009
"... Abstract We consider the portfolio selection problem in the accumulation phase of a defined contribution pension scheme in continuous time, and compare the meanvariance and the expected utility maximization approaches. Using the embedding technique pioneered by Zhou and Li ..."
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Abstract We consider the portfolio selection problem in the accumulation phase of a defined contribution pension scheme in continuous time, and compare the meanvariance and the expected utility maximization approaches. Using the embedding technique pioneered by Zhou and Li
Solving the NonLinear Dynamic Asset Allocation Problem: Effects of Arbitrary Stochastic
 Space. University of Connecticut, Department of Economics, Working paper
, 2009
"... In this paper we propose a methodology that we believe improves the effectiveness of several common assumptions underlying Modern Portfolio Theory’s dynamic optimization framework. The paper derives a general outline of a stochastic nonlinearquadratic control for analyzing and solving a nonlinea ..."
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In this paper we propose a methodology that we believe improves the effectiveness of several common assumptions underlying Modern Portfolio Theory’s dynamic optimization framework. The paper derives a general outline of a stochastic nonlinearquadratic control for analyzing and solving a nonlinear meanvariance optimization problem. The study first develops and then investigates the role of unsystematic (credit) risk in this continuous time stochastic asset allocation model where the wealth generating process has a nonnegative constraint. The paper finds that given unsystematic risk, wealth constraints and higher order moments the market price of risk is nonconstant and the investor’s optimal terminal return may be lower than previously indicated by a number of classical models. This result provides a convenient solution to practitioners seeking to evaluate competing