Risk and Decision Analysis

In this paper, we study the discounted free Gerber–Shiu function for the compound binomial risk model with by-claims and randomized dividend policy. Specifically, explicit expression for the discounted free Gerber–Shiu function is obtained. This result allows us to derive formulae for some useful insurance quantities, including the ruin probability, the probability function of the deficit at ruin, the joint probability function of the surplus immediately before ruin and the deficit at ruin, and the probability function of the claim causing ruin.

In this paper we derive a new class of time inconsistent dynamic coherent risk measures, allowing the interest rates involved to be random, which extends and modifies the results on risk measures in Appl. Anal. 86 (2007), 1429–1442. Since in this procedure one important mathematical tool is a kind of backward stochastic Volterra integral equations (BSVIEs in short) with stochastic Lipschitz coefficients, this paper firstly is devoted to develop the existence and uniqueness theory for the corresponding BSVIEs, which not only generalizes the results in Stoch. Proc. Appl. 116 (2006), 779–795; Appl. Anal. 86 (2007), 1429–1442; Probab. Theory Related Fields 142 (2008), 21–77; but also simplifies considerably the related arguments there.

In this paper, we study a mean–variance portfolio selection problem that has a probabilistic benchmark constraint. This constraint changes the problem into a non-convex one but could be solved via the method of Lagrange multipliers, whose existence is crucial in the solution.

The aim of this paper is to establish a tractable and flexible pricing model for Credit Contingent Interest Rate Swap (CCIRS), which is sensitive to interest rate and credit risk. Intensity-based approach is adopted to construct models for risk-free interest rate and default intensity. By using multi-factor Affine Jump Diffusion (AJD) process, a semi-close solution to the price of single-name CCIRS is derived. Further more, we put the counterparty risk into our pricing framework to compute the Credit Value Adjustment (CVA). Finally, numerical results and analysis have also been carried on.

We consider collocation method based on a piecewise polynomial approach in two spatial dimensions. Our model uses a finite element partition where the interpolation may be discontinuous across element boundaries. The underlying topological structure is the continuous or bounded functions with sup-norm. To ensure broad applicability we use a triangular finite element partition. We include a convergence result and examples. The examples include comparisons to finite element method and examples from finance.

In this paper, we propose a fast numerical method to evaluate discretely monitored derivatives. The key is to compute the involved probability integrals interactively. Our method can avoid the “curse of dimensionality” that most other methods suffer. Also, we give a constructive proof for explicit error estimation that based on a simple and systematic quadrature technique. The numerical frameworks are included for applications of barrier options on a stock and a short rate.