Rational hedging and valuation of integrated risks under constant absolute risk aversion

Becherer, Dirk

doi:10.1016/s0167-6687(03)00140-9

Cited by 93 publications

(138 citation statements)

References 43 publications

Supporting

Mentioning

134

Contrasting

Order By: Relevance

“…In this entropic case, this dilatation property has been referred to as volume scaling by Becherer (2003). Moreover, as noticed when studying the "toy model", the inf-convolution of two entropic risk measures is again an entropic risk measure.…”

Section: Dilatation Of Convex Risk Measures and Semi-group Propertiesmentioning

confidence: 96%

Inf-convolution of risk measures and optimal risk transfer

Barrieu¹,

2005

View full text Add to dashboard Cite

Abstract. We develop a methodology for optimal design of financial instruments aimed to hedge some forms of risk that is not traded on financial markets. The idea is to minimize the risk of the issuer under the constraint imposed by a buyer who enters the transaction if and only if her risk level remains below a given threshold. Both agents have also the opportunity to invest all their residual wealth on financial markets, but with different access to financial investments. The problem is reduced to a unique inf-convolution problem involving a transformation of the initial risk measures.

show abstract

Section: Dilatation Of Convex Risk Measures and Semi-group Propertiesmentioning

confidence: 96%

Inf-convolution of risk measures and optimal risk transfer

Barrieu¹,

2005

View full text Add to dashboard Cite

show abstract

“…Note that the inequality "Ä" is always true, while " " may not. This equality is shown by several authors in different settings, e.g., the case of no endowment .B Á 0) by Kramkov and Schachermayer [12] and Schachermayer [17], the case of bounded B by Bellini and Frittelli [2], and the case of exponential utility with suitably integrable B by Delbaen et al [5], Kabanov and Stricker [11] and Becherer [1]. Then a natural question arises: to what degree of generality does the equality (1.2) hold true ?…”

Section: Introductionmentioning

confidence: 85%

“…The "Six-Author Paper" [5] and its refinement [11] develop a general duality theory for the case of exponential utility: U.x/ D 1 e ˛x , giving the duality equality under (2.5) and the boundedness from above of B. This assumption is weakened by [1] to the condition corresponding to our (A4). More recently, Owari [13] extends this framework to the robust exponential utility maximization.…”

Section: Theorem 21 Under (A1) -(A4)mentioning

confidence: 99%

A Note on Utility Maximization with Unbounded Random Endowment

Owari

2010

Asia-Pac Financ Markets

View full text Add to dashboard Cite

This paper addresses the applicability of the convex duality method for utility maximization, in the presence of random endowment. When the price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true, for a wide class of utility functions and unbounded random endowments. We show this duality by exploiting Rockafellar's theorem on integral functionals, to a random utility function.

show abstract

“…Similar equations arise in other utility problems in incomplete markets, for example, in portfolio choice with recursive utility [32], valuation of mortgage-backed securities [34] and life-insurance problems [2]. first with It is worth noting, however, that the reaction-diffusion equation (45) does not belong to the class of such equations with Lipschitz reaction term.…”

Section: Single-name Casementioning

confidence: 95%

Utility valuation of multi-name credit derivatives and application to CDOs

Sircar

Zariphopoulou

2009

Quantitative Finance

View full text Add to dashboard Cite

We study the impact of risk-aversion on the valuation of credit derivatives. Using the technology of utility-indifference pricing in intensity-based models of default risk, we analyze resulting yield spreads in multiname credit derivatives, particularly CDOs. We study first the idealized problem with constant intensities where solutions are essentially explicit. We also give the large portfolio asymptotics for this problem. We then analyze the case where the firms have stochastic default intensities driven by a common factor, which can be viewed as another extreme from the independent case. This involves the numerical solution of a system of reaction-diffusion PDEs. We observe that the nonlinearity of the utility-indifference valuation mechanism enhances the effective correlation between the times of the credit events of the various firms leading to non-trivial senior tranche spreads, as often seen from market data.

show abstract

Rational hedging and valuation of integrated risks under constant absolute risk aversion

Cited by 93 publications

References 43 publications

Inf-convolution of risk measures and optimal risk transfer

Inf-convolution of risk measures and optimal risk transfer

A Note on Utility Maximization with Unbounded Random Endowment

Utility valuation of multi-name credit derivatives and application to CDOs

Contact Info

Product

Resources

About