Ordering Uncertain Options with Borrowing and Lending

Levy, Haim; Kroll, Yoram

doi:10.2307/2326569

Cited by 43 publications

(43 citation statements)

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“…Consequently, for any risk averse inventory manager with an increasing concave utility function, optimizing (2) guarantees a profit profile that is not strictly second order dominated by any other feasible profit profile. Interestingly, Theorem 2.1 (Levy and Kroll [19] …”

Section: Risk Averse Valuationsmentioning

confidence: 99%

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Risk Aversion in Inventory Management

Chen

Sim

Simchi‐Levi

et al. 2007

Operations Research

297

196

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Traditional inventory models focus on risk neutral decision makers, i.e., characterizing replenishment strategies that maximize expected total profit, or equivalently, minimize expected total cost over a planning horizon. In this paper, we propose a general framework for incorporating risk aversion in multi-period inventory models as well as multi-period models that coordinate inventory and pricing strategies. In each case, we characterize the optimal policy for various measures of risk that have been commonly used in the finance literature. In particular, we show that the structure of the optimal policy for a decision maker with exponential utility function is almost identical to the structure of the optimal risk neutral inventory (and pricing) policies. Computational results demonstrate the importance of this approach not only to risk averse decision makers, but also to risk neutral decision makers with limited information on the demand distribution.

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Section: Risk Averse Valuationsmentioning

confidence: 99%

“…We now experiment with the myopic CVaR inventory model of (19), for which a wealth independent (s, S) policy is optimal. Of course, being a myopic approach, we cannot guarantee that the policy derived from this method would lead to profit profile that is not second order stochastically dominated.…”

Section: Myopic Cvar Approachmentioning

confidence: 99%

Risk Aversion in Inventory Management

Chen

Sim

Simchi‐Levi

et al. 2007

Operations Research

297

196

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“…Following Levy and Kroll's (1978) quantile approach, the quantile of portfolio Z α of order P* conditional on realization y of Y can be written as…”

Section: Proofmentioning

confidence: 99%

“…The following proof of the quantile function of a portfolio composed of risky and risk-free assets is taken from Levy and Kroll (1978). Let X be an asset with a random return with a cdf F(X) and a quantile function X(P).…”

Section: Free Assetsmentioning

confidence: 99%

Analytical portfolio value-at-risk

Kaplanski¹

2005

JOR

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“…Additionally, it may be reconciled with the idea of maximizing expected utility. Levy and Kroll [LK78] show that for all utility functions U with the properties described in Section 2.1 and all random variables X and Y (representing losses) that…”

Section: Expected Shortfallmentioning

confidence: 99%

Financial Risk and Heavy Tails

Bradley

Taqqu

2003

Handbook of Heavy Tailed Distributions in Finance

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It is of great importance for those in charge of managing risk to understand how financial asset returns are distributed. Practitioners often assume for convenience that the distribution is normal. Since the 1960s, however, empirical evidence has led many to reject this assumption in favor of various heavy-tailed alternatives. In a heavy-tailed distribution the likelihood that one encounters significant deviations from the mean is much greater than in the case of the normal distribution. It is now commonly accepted that financial asset returns are, in fact, heavy-tailed. The goal of this survey is to examine how these heavy tails affect several aspects of financial portfolio theory and risk management. We describe some of the methods that one can use to deal with heavy tails and we illustrate them using the NASDAQ composite index.

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Ordering Uncertain Options with Borrowing and Lending

Cited by 43 publications

References 0 publications

Risk Aversion in Inventory Management

Risk Aversion in Inventory Management

Analytical portfolio value-at-risk

Financial Risk and Heavy Tails

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