Continuous time trading of a small investor in a limit order market

We provide a mathematical framework to model continuous time trading of a small investor in limit order markets. We show how elementary strategies can be extended in a suitable way to general continuous time strategies containing orders with infinitely many different limit prices. The general limit buy order strategies are predictable processes with values in the set of nonincreasing demand functions. It turns out that our strategy set of limit and market orders is closed, but limit orders can turn into market orders when passing to the limit, and any element can be approximated by a sequence of elementary strategies.     

Constructing sublinear expectations on path space

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G$G$-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G$G$-expectation, and an optional sampling theorem that holds without exceptional set. Our results also shed light on the inherent limitations to constructing sublinear expectations through aggregation.     

Mechanical response and texture evolution of AZ31 alloy at large strains for different strain rates and temperatures

In order to study the behavior of material under finite deformation at various strain rates, the responses of AZ31 Mg sheet are measured under uniaxial (tension and compression) and multiaxial (simple shear) loadings along rolling direction (RD), 45° to rolling direction (DD), 90° to rolling direction (TD), and normal to the sheet (ND) to large strains. The material exhibits positive strain rate sensitivity (SRS) at room and elevated temperatures; the SRS is more pronounced at high temperatures and lower strain rates. The r-value of the material under tensile loading at room temperatures is higher in TD at lower strain rate. Texture measurements on several failed specimens are reported under tension and simple shear after finite plastic deformation of about 20% equivalent strain. The as-received material exhibits a strong fiber with equal fractions of grains having the c-axis slightly tilted away from the sheet normal towards both +RD and −RD. Pole figures obtained after tensile loading along the rolling direction (RD) show that the texture of the material strengthens even at low strains, with c-axis perpendicular to the sheet plane and prism planes lining up in a majority of grains. However, the tensile loading axis along TD does not lead to similar texture strengthening; the c-axis distribution appears to be virtually unchanged from the virgin state. The pole figures obtained after in-plane compression along RD brings the c-axes of the grains parallel to the loading direction. The pole figures after simple shear loading show that the c-axis rotates to lie on the sheet plane consistent with a compression axis 45° away on the sheet plane.     

Optimal dividend and investing control of an insurance company with higher solvency constraints

This paper considers the optimal control problem of a large insurance company under a fixed insolvency probability. The company controls proportional reinsurance rate, dividend pay-outs and investing process to maximize the expected present value of the dividend pay-outs until the time of bankruptcy. This paper aims at describing the optimal return function as well as the optimal policy. As a by-product, the paper theoretically sets a risk-based capital standard to ensure the capital requirement that can cover the total risk.     

自动拨号报警图像监控系统的设计与实现

设计了一种图像监控系统,系统选取基于ARM7的处理器AT91SAM7x128,以μC/OS-II为操作系统.当系统巡逻信号被触发时,图像监控系统可以通过公用电话网自动拨号报警,图像可以通过串口摄像头模块C328采集,存储到U盘中.该设计突破了传统安防报警系统的设计思想,为家庭、店铺等终端用户提供了较好的图像监控系统解决方案.     

Remarks on some basic concepts in the KKM theory

In the KKM theory, some authors adopt the concepts of the compact closure (ccl), compact interior (cint), transfer compactly closed-valued multimap, transfer compactly l.s.c. multimap, and transfer compactly local intersection property, respectively, instead of the closure, interior, closed-valued multimap, l.s.c. multimap, and possession of a finite open cover property. In this paper, we show that such adoption is inappropriate and artificial. In fact, any theorem with a term with “transfer” attached is equivalent to the corresponding one without “transfer”. Moreover, we can invalidate terms with “compactly” attached by giving a finer topology on the underlying space. In such ways, we obtain simpler formulations of KKM type theorems, Fan-Browder type fixed point theorems, and other results in the KKM theory on abstract convex spaces.     

An integral representation approach for valuing American-style installment options with continuous payment plan

In this paper, we present an integral equation approach for the valuation of American-style installment derivatives when the payment plan is assumed to be a continuous function of the asset price and time. The contribution of this study is threefold. First, we show that in the Black-Scholes model the option pricing problem can be formulated as a free boundary problem under very general conditions on payoff structure and payment schedule. Second, by applying a Fourier transform-based solution technique, we derive a system of coupled recursive integral equations for the pair of free boundaries along with an analytic representation of the option price. Third, based on these results, we propose a unified framework which generalizes the existing methods and is capable of dealing with a wide range of monotonic payoff functions and continuous payment plans. Finally, by using the illustrative example of American vanilla installment call options, an explicit pricing formula is obtained for time-varying payment schedules.     

Gerber-Shiu analysis in a perturbed risk model with dependence between claim sizes and interclaim times

In this paper, we consider a compound Poisson risk model perturbed by a Brownian motion. We construct the bivariate cumulative distribution function of the claim size and interclaim time by Farlie-Gumbel-Morgenstern copula. The integro-differential equations and the Laplace transforms for the Gerber-Shiu functions are obtained. We also show that the Gerber-Shiu functions satisfy some defective renewal equations. For exponential claims, some explicit expressions are obtained, and numerical examples for the ruin probabilities are also given.     

Numerical solutions of quantile hedging for guaranteed minimum death benefits under a regime-switching jump-diffusion formulation

This work develops numerical approximation methods for quantile hedging involving mortality components for contingent claims in incomplete markets, in which guaranteed minimum death benefits (GMDBs) could not be perfectly hedged. A regime-switching jump-diffusion model is used to delineate the dynamic system and the hedging function for GMDBs, where the switching is represented by a continuous-time Markov chain. Using Markov chain approximation techniques, a discrete-time controlled Markov chain with two component is constructed. Under simple conditions, the convergence of the approximation to the value function is established. Examples of quantile hedging model for guaranteed minimum death benefits under linear jumps and general jumps are also presented.     

Symmetry analysis of a model of stochastic volatility with time-dependent parameters

We provide the solutions for the Heston model of stochastic volatility when the parameters of the model are constant and when they are functions of time. In the former case, the solution follows immediately from the determination of the Lie point symmetries of the governing 1+1 evolution partial differential equation. This is not the situation in the latter case, but we are able to infer the essential structure of the required nonlocal symmetry from that of the autonomous problem and hence can present the solution to the nonautonomous problem. As in the case of the standard Black-Scholes problem the presence of time-dependent parameters is not a hindrance to the demonstration of a solution.