89 research outputs found

    Counterparty risk valuation for CDS.

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    The valuation of counterparty risk for single name credit derivatives requires the computa- tion of joint distributions of default times of two default-prone entities. For a Merton-type model, we derive some formulas for these joint distribu- tions. As an application, closed formulas for counterparty risk on a CDS or for a first-to-default swap on two underlyings are obtained

    Hedging of Defaultable Contingent Claims using BSDE with uncertain time horizon.

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    This article focuses on the mathematical problem of existence and uniqueness of BSDE with a random terminal time which is a general random variable but not a stopping time, as it has been usually the case in the previous literature of BSDE with random terminal time. The main motivation of this work is a financial or actuarial problem of hedging of defaultable contingent claims or life insurance contracts, for which the terminal time is a default time or a death time, which are not stopping times. We have to use progressive enlargement of the Brownian filtration, and to solve the obtained BSDE under this enlarged filtration. This work gives a solution to the mathematical problem and proves the existence and uniqueness of solutions of such BSDE under certain general conditions. This approach is applied to the financial problem of hedging of defaultable contingent claims, and an expression of the hedging strategy is given for a defaultable contingent claim or a life insurance contract.

    Hedging of Defaultable Contingent Claims using BSDE with uncertain time horizon

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    This article focuses on the mathematical problem of existence and uniqueness of BSDE with a random terminal time which is a general random variable but not a stopping time, as it has been usually the case in the previous literature of BSDE with random terminal time. The main motivation of this work is a financial or actuarial problem of hedging of defaultable contingent claims or life insurance contracts, for which the terminal time is a default time or a death time, which are not stopping times. We have to use progressive enlargement of the Brownian filtration, and to solve the obtained BSDE under this enlarged filtration. This work gives a solution to the mathematical problem and proves the existence and uniqueness of solutions of such BSDE under certain general conditions. This approach is applied to the financial problem of hedging of defaultable contingent claims, and an expression of the hedging strategy is given for a defaultable contingent claim or a life insurance contract

    The density of the ruin time for a renewal-reward process perturbed by a diffusion

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    International audienceLet XX be a mixed process, sum of a brownian motion and a renewal-reward process, and τx\tau_{x} be the first passage time of a fixed level x<0x<0 by XX. We prove that τx\tau_x has a density and we give a formula for it. Links with ruin theory are presented. Our result may be computed in classical settings (for a Lévy or Sparre Andersen process) and also in a non markovian context with possible positive and negative jumps. Some numerical applications illustrate the interest of this density formula

    Optimal liquidation with additional information

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    International audienceWe consider the problem of how to optimally close a large assetposition in a market with a linear temporary price impact. We take the perspectiveof an agent who obtains a signal about the future price evolvement.By means of classical stochastic control we derive explicit formulas for the closingstrategy that minimizes the expected execution costs. We compare agentsobserving the signal with agents who do not see it. We compute explicitly theexpected additional gain due to the signal, and perform a comparative staticsanalysis

    The density of the ruin time for a renewal-reward process perturbed by a diffusion

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    Let XX be a mixed process, sum of a brownian motion and a renewal-reward process, and τx\tau_{x} be the first passage time of a fixed level $xRenewal-reward process ; Brownian motion ; Jump-diffusion process ; Time of ruin.

    Impact of Climate Change on HeatWave Risk

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    International audienceWe study a new risk measure inspired from risk theory with a heat wave risk analysis motivation. We show that this risk measure and its sensitivities can be computed in practice for relevant temperature stochastic processes. This is in particular useful for measuring the potential impact of climate change on heat wave risk. Numerical illustrations are given

    Robust optimization: a kriging-based multi-objective optimization approach

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    In the robust shape optimization context, the evaluation cost of numerical models is reduced by the use of a response surface. Multi-objective methodologies for robust optimization that consist in simultaneously minimizing the expectation and variance of a function have already been developed to answer to this question. However, efficient estimation in the framework of time-consuming simulation has not been completely explored. In this paper, a robust optimization procedure based on Taylor expansion, kriging prediction and a genetic NSGA-II algorithm is proposed. The two objectives are the Taylor expansion of expectation and variance. The kriging technique is chosen to surrogate the function and its derivatives. Afterwards, NSGA-II is performed on kriging response surfaces or kriging expected improvements to construct a Pareto front. One point or a batch of points is chosen carefully to enrich the learning set of the model. When the budget is reached the non-dominated points provide designs that make compromises between optimization and robustness. Seven relevant strategies based on this main procedure are detailed and compared in two test functions (2D and 6D). In each case, the results are compared when the derivatives are observed and when they are not. The procedure is also applied to an industrial case study where the objective is to optimize the shape of a motor fan

    Max-Min optimization problem for Variable Annuities pricing

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    International audienceWe study the valuation of variable annuities for an insurer. We concentrate on two types of these contracts that are the guaranteed minimum death benefits and the guaranteed minimum living benefits ones and that allow the insured to withdraw money from the associated account. As for many insurance contracts, the price of variable annuities consists in a fee, fixed at the beginning of the contract, that is continuously taken from the associated account. We use a utility indifference approach to determine this fee and, in particular, we consider the indifference fee rate in the worst case for the insurer i.e. when the insured makes the withdrawals that minimize the expected utility of the insurer. To compute this indifference fee rate, we link the utility maximization in the worst case for the insurer to a sequence of maximization and minimization problems that can be computed recursively. This allows to provide an optimal investment strategy for the insurer when the insured follows the worst withdrawals strategy and to compute the indifference fee. We finally explain how to approximate these quantities via the previous results and give numerical illustrations of parameter sensibility

    Quadratic BSDEs with single jump and applications

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