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Indifference pricing with counterparty risk

Ngo M., Nguyen T., Duong T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2017

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Vol. 65, nr 5

695--702

EN

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 to solving just 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 jump’s size, intensity of the default, absolute risk aversion and change in the underlying volatility.

2

Bi-dimensional composition with domain specific languages

Ionita A. D., Estublier J., Leveque T., Nguyen T.

e-Informatica Software Engineering Journal

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2009

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Vol. 3, nr 1

27--41

EN

The paper presents how domain modeling may leverage the hierarchical composition, supporting two orthogonal mechanisms (vertical and horizontal) for composing completely autonomous parts. The vertical mechanism is in charge of coordinating heterogeneous components, tools or services at a high level of abstraction, by hiding the technical details. The result of such a composition is called "domain" and represents a high granularity unit of reuse, which may be easily developed in Mélusine framework. A domain is characterised by a Domain Specific Language (DSL) and applications in that domain are defined by models executed by the DSL interpreter. Most often, this is significantly simpler than writing a program using a general purpose language. Unfortunately, DSLs have a narrow scope, while real world applications usually span over many domains, raising the issue of domain (and DSL) composition. To overcome this problem, the horizontal mechanism composes domains at the level of their DSLs, even if they have been independently designed and implemented. The paper presents a model and metamodel perspective of the Mélusine bi-dimensional composition, assisted and automated with the Codele tool, which allows specification at a high level of abstraction, followed by Java and AspectJ code generation.

3

A robust tracking control scheme for a class of nonlinear systems with fuzzy nominal model

Mei F., Zhihong M., Yu X., Nguyen T.

Applied Mathematics and Computer Science

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1998

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Vol. 8, no 1

145-158

EN

A novel robust tracking control scheme is proposed for a class of nonlinear systems. It is shown that a nonlinear system is first approximated by a fuzzy nominal model by aggregating a set of linearized local subsystems and then a conventional linear feedback controller is designed to stabilise the nominal system. In order to obtain good tracking performance for the controlled nonlinear system, a variable structure compensator is introduced to eliminate the effects or the approximation error and uncertainties between the fuzzy nominal model and the nonlinear system. A simulation example using a one-link rigid robotic manipulator is given in support of the proposed control scheme.