Optimal investment under multiple defaults risk: A BSDE-decomposition approach

Jiao, Ying; Kharroubi, Idris; Pham, Huyên

doi:10.1214/11-aap829

Cited by 53 publications

(62 citation statements)

References 14 publications

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“…alculation of the ) for our pricing n the coefficients the counterparty. e can reduce the one optimal conexponential utilition of the value [4], which sepaal before-default by considering a SDE). We solve al utility function is influenced by et experiences not ift and/or volatilays out the model t zon T < ∞ and its natural filtration F = (F t ), t ∈ [0, T ] satisfying the usual conditions of right-continuity and completeness.…”

Section: Basic Definition and Hypothesismentioning

confidence: 99%

“…tribution in this paper is the calculation of the py martingale measure (MEMM) for our pricing included a jump and changes in the coefficients rocess after the default time of the counterparty. MEMM and the result in [3], we can reduce the rence pricing problem to just one optimal connd utilize its advantages for an exponential utilWe then employ the decomposition of the value e and after default proposed by [4], which sepalem into after-default and global before-default and solves each subproblem by considering a chastic differential equation (BSDE). We solve ifference price with exponential utility function option whose underlying asset is influenced by isk in which the underlying asset experiences not jump but also changes in its drift and/or volatiltructured as follows.…”

Section: Basic Definition and Hypothesismentioning

confidence: 99%

“…eled more efficiently rated in [4,5]. varying, begun to be e order behavior can when system's proptions.…”

Section: Basic Definition and Hypothesismentioning

confidence: 99%

“…Fractional calculus has been ent tool to model behavior of many materials rticularly those involving diffusion processes. racapacitors can be modeled more efficiently calculus, as was demonstrated in [4,5]. case when order is time-varying, begun to be ly.…”

Section: Minimal Entropy Martingale Measure and Its Relation To Indifmentioning

confidence: 99%

“…We can see from (4,5) and (6) that the dynamics of the discounted stock price process S can be written as:…”

Section: Introductionmentioning

confidence: 99%

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Indifference pricing with counterparty risk

Ngo

Nguyen

Duong

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. We present counterparty risk by a jump in the underlying price and a structural change of the price process after the default of the counterparty. The default time is modeled by a default-density approach. Then we study an exponential utility-indifference price of an European option whose underlying asset is exposed to this counterparty risk. Utility-indifference pricing method normally consists in solving two optimization problems. However, by using the minimal entropy martingale measure, we reduce it to solving only one optimal control problem. In addition, to overcome the incompleteness obstacle generated by the possible jump and the change in structure of the price process, we employ the BSDE-decomposition approach in order to decompose the problem into a global-before-default optimal control problem and an after-default one. Each problem works in its own complete framework. We demonstrate the result by numerical simulation of an European option price under the impact of the size of the jump, intensity of the default, absolute risk aversion and change in the underlying volatility. problem and utilize its advantages for an exponential utility function. We then employ the decomposition of the value function before and after default proposed by [4], which separates the problem into after-default and global before-default subproblems, and solves each subproblem by considering a backward stochastic differential equation (BSDE). We solve the utility-indifference price with exponential utility function for a vanilla option whose underlying asset is influenced by counterparty risk in which the underlying asset experiences not only a jump in price, but also changes in its drift and/or volatility.The paper is structured as follows. Section 2 lays out the model and the option pricing problem with a default density hypothesis. In Section 3 we present the minimal entropy martingale measure approach (MEMM) to solve the utility-difference pricing problem as well as the resulting MEMM density of our problem. Once we have this MEMM density, the option price is obtained using the decomposition approach and the BSDE calculation in Section 4. Finally we demonstrate the numerical simulation of a basic European option in Section 5. Basic definition and hypothesisIn our model, the risky asset subject to a counterparty risk is denoted by a stochastic process S = (S t ) t ¸ 0 . Our objective is to calculate the price of an European derivative (option) mature at a finite time horizon T on this security.We consider a probability space (Ω, Indifference pricing with counterparty riskAbstract. We present counterparty risk by a jump in the underlying price and a structural change of the price process after the default of the counterparty. The default time is modeled by a default-density approach. Then we study an exponential utility-indifference price of an European option whose underlying asset is exposed to this counterparty risk. Utility-indifference pricing method normally consists in solving two optimization problems. Howev...

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Section: Basic Definition and Hypothesismentioning

confidence: 99%

Section: Basic Definition and Hypothesismentioning

confidence: 99%

“…eled more efficiently rated in [4,5]. varying, begun to be e order behavior can when system's proptions.…”

Section: Basic Definition and Hypothesismentioning

confidence: 99%

Section: Minimal Entropy Martingale Measure and Its Relation To Indifmentioning

confidence: 99%

“…We can see from (4,5) and (6) that the dynamics of the discounted stock price process S can be written as:…”

Section: Introductionmentioning