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Maximizing the growth rate under risk constraints
, 2007
"... We investigate the ergodic problem of growthrate maximization under a class of risk constraints in the context of incomplete, Itôprocess models of financial markets with random ergodic coefficients. Including valueatrisk (VaR), tailvalueatrisk (TVaR), and limited expected loss (LEL), these co ..."
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We investigate the ergodic problem of growthrate maximization under a class of risk constraints in the context of incomplete, Itôprocess models of financial markets with random ergodic coefficients. Including valueatrisk (VaR), tailvalueatrisk (TVaR), and limited expected loss (LEL), these constraints can be both wealthdependent (relative) and wealthindependent (absolute). The optimal policy is shown to exist in an appropriate admissibility class, and can be obtained explicitly by uniform, statedependent scaling down of the unconstrained (Merton) optimal portfolio. This implies that the riskconstrained wealthgrowth optimizer locally behaves like a CRRAinvestor, with the relative riskaversion coefficient depending on the current values of the market coefficients.
CRRA UTILITY MAXIMIZATION UNDER DYNAMIC RISK CONSTRAINTS
, 2013
"... The problem of optimal investment with CRRA (constant, relative risk aversion) preferences, subject to dynamic risk constraints on trading strategies, is the main focus of this paper. Several works in the literature, which deal either with optimal trading under static risk constraints or with VaR{b ..."
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The problem of optimal investment with CRRA (constant, relative risk aversion) preferences, subject to dynamic risk constraints on trading strategies, is the main focus of this paper. Several works in the literature, which deal either with optimal trading under static risk constraints or with VaR{based dynamic risk constraints, are extended. The market model considered is continuous in time and incomplete, and the prices of nancial assets are modeled by Ito ̂ processes. The dynamic risk constraints, which are time and state dependent, are generated by a general class of risk measures. Optimal trading strategies are characterized by a quadratic BSDE. Within the class of time consistent distortion risk measures, a three{fund separation result is established. Numerical results emphasize the eects of imposing risk constraints on trading.
Risk minimization and portfolio diversification
, 2014
"... We consider the risk minimization problem, with capital at risk as the coherent measure, under the BlackScholes setting. The problem is studied, when there exists additional correlation constraint between the desired portfolio and another financial index, and the closed form solution for the optim ..."
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We consider the risk minimization problem, with capital at risk as the coherent measure, under the BlackScholes setting. The problem is studied, when there exists additional correlation constraint between the desired portfolio and another financial index, and the closed form solution for the optimal portfolio is obtained. We also mention to variance reduction and getting better diversified portfolio as the applications of correlation condition in this paper. 1
Dynamic optimal portfolios benchmarking the stock market
"... The paper investigates dynamic optimal portfolio strategies of utility maximizing portfolio managers in the presence of risk constraints. Especially we consider the risk, that the terminal wealth of the portfolio falls short of a certain benchmark level which is proportional to the stock price. Th ..."
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The paper investigates dynamic optimal portfolio strategies of utility maximizing portfolio managers in the presence of risk constraints. Especially we consider the risk, that the terminal wealth of the portfolio falls short of a certain benchmark level which is proportional to the stock price. This risk is measured by the Expected Utility Loss. We generalize the findings our previous papers to this case. Using the BlackScholes model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Numerical examples illustrate the analytic results.
Analysis of portfolio optimization with and without shortselling under Capital at Risk
, 2006
"... We consider a continuoustime portfolio problem with a capital at risk (CaR) constraint for constant portfolio processes. We get closedform solutions and compare these with solutions for the meanvariance problem. Also, the portfolio problem under CaR with shortselling constraints is solved. Furth ..."
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We consider a continuoustime portfolio problem with a capital at risk (CaR) constraint for constant portfolio processes. We get closedform solutions and compare these with solutions for the meanvariance problem. Also, the portfolio problem under CaR with shortselling constraints is solved. Furthermore, we show that capital at risk is not a coherent risk measure. 2