L^(p)-solutions of Multi-dimensional Oblique Reflected BSDEs and Optimal Switching Problem on Finite or Infinite Time Horizon

In this paper,we study mulit-dimensional oblique reflected backward stochastic differential equations(RBSDEs)in a more general framework over finite or infinite time horizon,corresponding to the pricing problem for a type of real option.We prove that the equation can be solved uniquely in L^(p)(1<p≤2)-space,when the generators are uniformly continuous but each component taking values independently.Furthermore,if the generator of this equation fulfills the infinite time version of Lipschitzian continuity,we can also conclude that the solution to the oblique RBSDE exists and is unique,despite the fact that the values of some generator components may affect one another.

The Convergence Rate from Discrete to Continuous Optimal Investment Stopping Problem

The author studies the optimal investment stopping problem in both continuous and discrete cases, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal wealth.Based on the work of Hu et al.(2018) with an additional stochastic payoff function,the author characterizes the value function for the continuous problem via the theory of quadratic reflected backward stochastic differential equations(BSDEs for short) with unbounded terminal condition. In regard to the discrete problem, she gets the discretization form composed of piecewise quadratic BSDEs recursively under Markovian framework and the assumption of bounded obstacle, and provides some useful a priori estimates about the solutions with the help of an auxiliary forward-backward SDE system and Malliavin calculus. Finally, she obtains the uniform convergence and relevant rate from discretely to continuously quadratic reflected BSDE, which arise from corresponding optimal investment stopping problem through above characterization.

Optimal stopping of multi-project software testing in the context of software cybernetics

Software cybernetics explores the interplay between control theory/engineering and software theory/engineering. The controlled Markov chains (CMC) approach to software testing follows the idea of software cybernetics and treats software testing as a control problem. The software under test serves as a controlled object and the software testing strategy serves as the corresponding controller. The software under test and the software testing strategy make up a closed-loop feedback control system, and the theory of controlled Markov chains can be used to design and optimize software testing strategies in accordance with testing/reliability goals given a priori. In this paper we apply the CMC approach to the optimal stopping problem of multi-project software testing. The problem under consideration assumes that a single stopping action can stop testing of all the software systems under test simultaneously. The theoretical results presented in this paper describe how to test multiple software systems and when to stop testing in an optimal manner. An illustrative example is used to explain the theoretical results. The study of this paper further justifies the effectiveness of the CMC approach to software testing in particular and the idea of software cybernetics in general.

The pricing of perpetual convertible bond with credit risk

Convertible bond gives holder the right to choose a conversion strategy to maximize the bond value, and issuer also has the right to minimize the bond value in order to maximize equity value. When there is default occurring, conversion and calling strategies are invalid. In the framework of reduced form model, we reduce the price of convertible bond to variational inequalities, and the coefficients of variational inequalities are unbounded at the original point. Then the existence and uniqueness of variational inequality are proven. Finally, we prove that the conversion area, the calling area and the holding area are connected subsets of the state space.

Efficient Numerical Valuation of Continuous Installment Options

In this work we investigate the novel Kryzhnyi method for the numerical inverse Laplace transformation and apply it to the pricing problem of continuous installment options.We compare the results with the one obtained using other classical methods for the inverse Laplace transformation,like the Euler summation method or the Gaver-Stehfest method.