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进一步讨论了系数b(t,y,q,p,ω)关于|q|为平方增长的倒向随机微分方程(BSDE):Yt=Y ∫Tb(s,ys,qs,p-s,ω)ds-∫T t∫zP~s(z)Ⅱ(dz)ds-∫Tt~qsdws-∫Ttzp~s(z)N~k(ds,dz),t∈[0,T];及反射BSDE的解的极限定理、解的比较定理及解的惟一性定理.并分别给出了例子. 相似文献
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讨论了系数关于q为平方增长,p和-y为指数增长的带跳倒向随机微分方程(BSDE)解的存在性,以及有这种系数的反射BSDE解的存在性. 相似文献
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We solve a mean-variance hedging problem in an incomplete market where multiple defaults can occur. For this purpose, we use a default-density modeling approach. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the dependence of the default times is modelled using a conditional density hypothesis. We prove the quadratic form of each value process between consecutive default times and recursively solve systems of coupled quadratic backward stochastic differential equations (BSDEs). We demonstrate the existence of these solutions using BSDE techniques. Then, using a verification theorem, we prove that the solutions of each subcontrol problem are related to the solution of our global mean-variance hedging problem. As a byproduct, we obtain an explicit formula for the optimal trading strategy. Finally, we illustrate our results for certain specific cases and for a multiple defaults case in particular. 相似文献
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We examine the connections between a novel class of multi-person stopping games with redistribution of payoffs and multi-dimensional reflected BSDEs in discrete- and continuous-time frameworks. Our goal is to provide an essential extension of classic results for two-player stopping games (Dynkin games) to the multi-player framework. We show the link between certain multi-period m-player stopping games and a new kind of m-dimensional reflected BSDEs. The existence and uniqueness of a solution to continuous-time reflected BSDEs are established. Continuous-time redistribution games are constructed with the help of reflected BSDEs and a characterization of the value of such stopping games is provided. 相似文献
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本文讨论了如下的由Levy过程驱动的倒向随机微分方程适应解的存在唯一性■其中W_s是一Wiener过程,H_s为由Levy过程构成Teugels鞅.我们通过构造函数逼近序列的方法证明了,在漂移系数f关于Y满足随机单调,f关于Z和U满足随机Lipschitz条件下,方程存在唯一适应解. 相似文献
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We study a finite-dimensional continuous-time optimal control problem on finite horizon for a controlled diffusion driven by Brownian motion, in the linear-quadratic case. We admit stochastic coefficients, possibly depending on an underlying independent marked point process, so that our model is general enough to include controlled switching systems where the switching mechanism is not required to be Markovian. The problem is solved by means of a Riccati equation, which turned out to be a backward stochastic differential equation driven by the Brownian motion and by the random measure associated with the marked point process. 相似文献
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