Mean-Variance Hedging on Uncertain Time Horizon in a Market with a Jump

Kharroubi, Idris; Lim, Thomas; Ngoupeyou, Armand

doi:10.1007/s00245-013-9213-5

Cited by 39 publications

(51 citation statements)

References 18 publications

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“…The proof follows similar arguments as in Kharroubi and Lim (2014) and Kharroubi et al (2013). The major difference is that we distinguish two cases corresponding to the sets {τ 1 < τ 2 } and {τ 2 < τ 1 }.…”

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confidence: 83%

A Model-Point Approach to Indifference Pricing of Life Insurance Portfolios with Dependent Lives

Blanchet-Scalliet

Dorobantu

Salhi

2017

Methodol Comput Appl Probab

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In this paper, we study the pricing of life insurance portfolios in the presence of dependent lives. We assume that an insurer with an initial exposure to n mortality-contingent contracts wanted to acquire a second portfolio constituted of m individuals. The policyholders' lifetimes in these portfolios are correlated with a Farlie-Gumbel-Morgenstern (FGM) copula, which induces a dependency between the two portfolios. In this setting, we compute the indifference price charged by the insurer endowed with an exponential utility. The optimal price is characterized as a solution to a backward differential equation (BSDE). The latter can be decomposed into (n − 1)n! auxiliary BSDEs. In this general case, the derivation of the indifference price is computationally infeasible. Therefore, while focusing on the example of death benefit contracts, we develop a model point based approach in order to ease the computation of the price. It consists on replacing each portfolio with a single policyholder that replicates some risk metrics of interest. Also, the two representative agents should adequately reproduce the observed dependency between the initial portfolios.

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confidence: 83%

A Model-Point Approach to Indifference Pricing of Life Insurance Portfolios with Dependent Lives

Blanchet-Scalliet

Dorobantu

Salhi

2017

Methodol Comput Appl Probab

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“…Some attention has also been given to the so-called stochastic Lipschitz case, where the generator is Lipschitz continuous in (y, z) but with constants which are actually random processes themselves. There are few papers going in this direction, among which we can Blanchet-Scalliet and Eyraud-Loisel [1], Lim and Quenez [109], Jenablanc, Matoussi and Ngoupeyou [89], Kharroubi, Quenez and Sulem [127], Lim and Ngoupeyou [96], Kharroubi and Lim [95], Laeven and Stadje [105], Richter [130], Jeanblanc, Mastrolia, Possamaï and Réveillac [88], Kazi-Tani, Possamaï and Zhou [93,94], Fujii and Takahashi [71], Dumitrescu, Quenez and Sulem [58], and El Karoui, Matoussi and Ngoupeyou [61], while the specific case of Lévy processes was treated by Nualart and Schoutens [123] and later Bahlali, Eddahbi and Essaky [5]. A general presentation has been proposed recently by Kruse and Popier [102,103], to which we refer for more references (see also the recent paper of Yao [140]).…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness results for BSDE with jumps: the whole nine yards

Papapantoleon¹,

Possamaï²,

Saplaouras³

2018

Electron. J. Probab.

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This paper is devoted to obtaining a wellposedness result for multidimensional BSDEs with possibly unbounded random time horizon and driven by a general martingale in a filtration only assumed to satisfy the usual hypotheses, i.e. the filtration may be stochastically discontinuous. We show that for stochastic Lipschitz generators and unbounded, possibly infinite, time horizon, these equations admit a unique solution in appropriately weighted spaces. Our result allows in particular to obtain a wellposedness result for BSDEs driven by discrete-time approximations of general martingales.2010 Mathematics Subject Classification. 60G48, 60G55, 60G57, 60H05. Key words and phrases. BSDEs, processes with jumps, stochastically discontinuous martingales, random time horizon, stochastic Lipschitz generator. We thank Martin Schweizer, two anonymous referees and the associate editor for their comments that have resulted in a significant improvement of the manuscript. Alexandros Saplaouras gratefully acknowledges the financial support from the DFG Research Training Group 1845 "Stochastic Analysis with Applications in Biology, Finance and Physics". Dylan Possamaï gratefully acknowledges the financial support of the ANR project PACMAN, ANR-16-CE05-0027. Moreover, all authors gratefully acknowledge the financial support from the PROCOPE project "Financial markets in transition: mathematical models and challenges". 1 The authors are indebted to Saïd Hamadène for pointing out this reference. The published version of [51] states that the article was received on October 27, 1971. It is also present in the bibliography of [21], though it is never referred to in the text. 2 We emphasize that the references given below are just the tip of the iceberg, though most of them are, in our view, among the major ones of the field. Nonetheless, we do not make any claim about comprehensiveness of the following list. 1 2 A. PAPAPANTOLEON, D. POSSAMAÏ, AND A. SAPLAOURAS mention El Karoui and Huang [60], Bender and Kohlmann [18], Wang, Ran and Chen [138] as well as Briand and Confortola [27]. The first results going beyond the linear growth assumption in z, which assumed quadratic growth, were obtained independently by Kobylanski [97, 98, 99] and Dermoune, Hamadène and Ouknine [56], for bounded ξ and f Lipschitz in y. These results were then further studied by Eddhabi and Ouknine [59], and improved by Lepeltier and San Martín [107, 108], Briand, Lepeltier and San Martín [35] and revisited by Briand and Élie [31], but still for bounded ξ. Wellposedness in the quadratic case when ξ has sufficiently large exponential moments was then investigated by Briand and Hu [33, 34], followed by Delbaen, Hu and Richou [54, 55], Essaky and Hassani [66], and Briand and Richou [36]. A specific quadratic setting with only square integrable terminal conditions has been considered recently by Bahlali, Eddahbi and Ouknine [6, 7], while a result with logarithmic growth was also obtained by Bahlali and El Asri [8], and Bahlali, Kebiri, Khelfallah and Moussaoui [13]. The ca...

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“…In the optimization problem with random default times, it is often supposed that the random time satisfies the intensity hypothesis (e.g., Lim and Quenez (2011) and Kharroubi et al (2013)) or the density hypothesis (e.g., Blanchet-Scalliet et al (2008), Jeanblanc et al (2015), and Jiao et al (2013)), so that it is a totally inaccessible stopping time in the market filtration. In particular, in Jiao et al (2013), we consider marked random times where the random mark represents the loss at default and we suppose that the vector of default time and mark admits a conditional density.…”

Section: Introductionmentioning

confidence: 99%

Information uncertainty related to marked random times and optimal investment

Jiao

Kharroubi

2018

Probab Uncertain Quant Risk

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which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. AbstractWe study an optimal investment problem under default risk where related information such as loss or recovery at default is considered as an exogenous random mark added at default time. Two types of agents who have different levels of information are considered. We first make precise the insider's information flow by using the theory of enlargement of filtrations and then obtain explicit logarithmic utility maximization results to compare optimal wealth for the insider and the ordinary agent.

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Mean-Variance Hedging on Uncertain Time Horizon in a Market with a Jump

Cited by 39 publications

References 18 publications

A Model-Point Approach to Indifference Pricing of Life Insurance Portfolios with Dependent Lives

A Model-Point Approach to Indifference Pricing of Life Insurance Portfolios with Dependent Lives

Existence and uniqueness results for BSDE with jumps: the whole nine yards

Information uncertainty related to marked random times and optimal investment

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