A Delayed Black and Scholes Formula I

In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to fit real market data, and is yet simple enough to allow for a closed-form representation of the option price. Furthermore, the model maintains the no-arbitrage property and the completeness of the market. The derivation of the option-pricing formula is based on an equivalent martingale measure

Stability of some linear systems with delays

International audienceAsymptotic stability of a class of linear equations with arbitrary discrete and distributed delays is investigated. Both delay-independent and delay-dependent stability conditions are formulated in terms of existence of positive definite solutions to Riccati matrix equations. The approach of deriving various Riccati equations using the direct Lyapunov method is proposed

Estimation of the solutions of Volterra difference equations

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Estimate of solutions for some Volterra difference equations

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Mean square stability of difference equations with a stochastic delay

International audienceThe paper describes mean-square stability conditions for nonlinear delay difference equations with a stochastic delay. The first part develops a formula for the infinitesimal operator. Using this formula asymptotic mean square stability conditions are derived. A final example is provided

About stability of some functional differential equations of neutral type

The method of construction of Liapunov functionals for some equations of neutral type with arbitrary delay (or arbitrary after-effect) is proposed. This method allows us to obtain stability conditions formulated immediately in terms of the characteristics concerning the equations under consideration. Equations of second and third order, non-linear systems and predator-prey systems are considered in detail as examples

Stability of nonlinear differential equations with distributed delay

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