This paper derives the optimal debt ratio and dividend payment strategies for an insurance company. Taking into account the impact of reinsurance policies and claims from the credit derivatives, the surplus process is stochastic that is jointly determined by the reinsurance strategies, debt levels, and unanticipated shocks. The objective is to maximize the total expected discounted utility of d...

In this paper, we study a type of reflected BSDE with a constraint and introduce a new kind of nonlinear expectation via BSDE with a constraint and prove the Doob-Meyer decomposition with respect to the super(sub)martingale introduced by this nonlinear expectation. Then we an application on the pricing of American options in incomplete market.

We study a class of nonlinear BSDEs with superlinear driver process f adapted to filtration F and over random time interval [[0, S]] where S is stopping F. The terminal condition $\xi$ allowed take the value +$\infty$, i.e., singular. Our goal show existence solutions BSDE in this setting. will do so by proving that minimal supersolution solution, attains values probability 1. consider three ty...

and Applied Analysis 3 where fM sup{f x, t | x, t ∈ Ω × }, fl inf{f x, t | x, t ∈ Ω × }, we show that the generalized solution is uniformly bounded. At last, by the method of monotone iteration, we establish the existence of the nontrivial periodic solutions of the system 1.1 1.2 , which follows from the existence of a pair of large periodic supersolution and small periodic subsolution. At last...

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Let Ω be a domain in Rd, d ≥ 2, and 1 < p <∞. Fix V ∈ Lloc(Ω). Consider the functional Q and its Gâteaux derivative Q′ given by Q(u) := ∫ Ω (|∇u|+V |u|)dx, 1 p Q(u) := −∇·(|∇u|∇u)+V |u|u. If Q ≥ 0 on C∞ 0 (Ω), then either there is a positive continuous function W such that ∫ W |u|p dx ≤ Q(u) for all u ∈ C∞ 0 (Ω), or there is a sequence uk ∈ C ∞ 0 (Ω) and a function v > 0 satisfying Q ′(v) = 0, ...

We consider a two-dimensional optimal dividend problem in the context of two insurance companies with compound Poisson surplus processes, who collaborate by paying each other’s deficit when possible. We solve the stochastic control problem of maximizing the weighted sum of expected discounted dividend payments (among all admissible dividend strategies) until ruin of both companies, by extending...

In this paper we consider an optimal dividend problem for an insurance company which risk process evolves as a spectrally negative Lévy process (in the absence of dividend payments). We assume that the management of the company controls timing and size of dividend payments. The objective is to maximize the sum of the expected cumulative discounted dividends received until the moment of ruin and...

The shape-from-shading (SfS) problem in computer vision is to compute at hand of the shading variation in a given 2-D image the 3-D structure of depicted objects. We introduce an efficient numerical method for a new perspective SfS model for general non-Lambertian surfaces. First, the modelling process is given in detail. The model is based on the perspective model for Lambertian surfaces recen...