Conditional Default Probability and Density

Jeanblanc, Monique; Jiao, Ying; Zargari, B.

doi:10.1007/978-3-319-02069-3_9

Cited by 9 publications

(9 citation statements)

References 12 publications

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“…Moreover, by considering a conditional density, and thus a time-dependence of the martingale density process (α t (θ, ℓ)) t≥0 , we embed the relevant case in practice when the default times are not independent of the reference market information F. Compared to the classical default intensity processes for successive defaults in the top-down modeling approach, the conditional density provides more and necessary information for analyzing the impact of default events. Further detailed discussion and some explicit models for density of ordered random times are given in [5].…”

Section: Multiple Defaults Modelmentioning

confidence: 99%

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

Jiao¹,

Kharroubi²,

Pham³

2013

Ann. Appl. Probab.

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We study an optimal investment problem under contagion risk in a financial model subject to multiple jumps and defaults. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the dependence of default times is modeled by a conditional density hypothesis. In this Itô-jump process model, we give a decomposition of the corresponding stochastic control problem into stochastic control problems in the default-free filtration, which are determined in a backward induction. The dynamic programming method leads to a backward recursive system of quadratic backward stochastic differential equations (BSDEs) in Brownian filtration, and our main result proves, under fairly general conditions, the existence and uniqueness of a solution to this system, which characterizes explicitly the value function and optimal strategies to the optimal investment problem. We illustrate our solutions approach with some numerical tests emphasizing the impact of default intensities, loss or gain at defaults and correlation between assets. Beyond the financial problem, our decomposition approach provides a new perspective for solving quadratic BSDEs with a finite number of jumps.

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Section: Multiple Defaults Modelmentioning

confidence: 99%

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

Jiao¹,

Kharroubi²,

Pham³

2013

Ann. Appl. Probab.

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“…Let F be a Brownian ltration and G its progressive enlargement with a strictly positive random time τ ∈ F ∞ satisfying Jacod's absolute continuity assumption (5.16) with some density α t (u), t, u ≥ 0. Such a random time can be dened as τ := ψ( ∞ 0 f (t)dB t ), where ψ is a dierentiable, positive and strictly increasing function, and B is a real valued standard F-Brownian motion (see [EKJJZ14]). Let X be the compensated…”

Section: Examplesmentioning

confidence: 99%

Semimartingales and shrinkage of filtration

et al. 2021

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We consider a complete probability space (Ω, F, P), which is endowed with two ltrations, G and F, assumed to satisfy the usual conditions and such that F ⊂ G. On this probability space we consider a real valued special G-semimartingale X. The results can be generalized to the case of R n valued special semimartingales, in a straightforward manner. We x a truncation function with respect to which the semimartingale characteristics are computed.The purpose of this work is to study the following two problems:A. If X is F-adapted, compute the F-semimartingale characteristics of X in terms of the G-semimartingale characteristics of X.

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“…• In the particular case where the F t -conditional law of L admits a density g t (l) w.r.t. the Lebesgue measure, the default density can be completely deduced (see [6,Proposition 3]) in this framework as α t (θ) = λ θ g t (Λ θ ), t ≥ θ and α t (θ) = E[α θ (θ)|F t ], t ≤ θ where λ is the process given in Section 2.…”

Section: Remark 43mentioning

confidence: 99%

Portfolio optimization with insider’s initial information and counterparty risk

Hillairet

Jiao

2014

Finance Stoch

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We study the gain of an insider having private information which concerns the default risk of a counterparty. More precisely, the default time τ is modelled as the first time a stochastic process hits a random barrier L. The insider knows this barrier (as it can be the case for example for the manager of the counterparty), whereas standard investors only observe its value at the default time. All investors aim to maximize the expected utility from terminal wealth, on a financial market where the risky asset price is exposed to a sudden loss at the default time of the counterparty. In this framework, the insider's information is modelled by using an initial enlargement of filtration and τ is a stopping time with respect to this enlarged filtration. We prove that the regulator must impose short selling constraints for the insider, in order to exclude the value process to reach infinity. We then solve the optimization problem and we study the gain of the insider, theoretically and numerically. In general, the insider achieves a larger value of expected utility than the standard investor. But in extreme situations for the default and loss risks, a standard investor may in average outperform the insider, by taking advantage of an aggressive short selling position which is not allowed for the insider, but at the risk of big losses if the default finally occurs after the maturity.Keywords : asymmetric information, enlargement of filtrations, counterparty risk, optimal investment, duality, dynamic programming.MSC 2010 : 60H30 91B28 91G40 93E20 * This research is part of a project of Europlace Institute of Finance. We thank

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Conditional Default Probability and Density

Cited by 9 publications

References 12 publications

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

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

Semimartingales and shrinkage of filtration

Portfolio optimization with insider’s initial information and counterparty risk

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