Browsing by Author "Siu, Tak Kuen"
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- ItemOpen AccessBackward Stochastic Difference Equations for Dynamic Convex Risk Measures on a Binomial Tree(Applied Probability Trust, 2014-08-04) Elliott, Robert J.; Siu, Tak Kuen; Cohen, Samuel N.Using backward stochastic difference equations (BSDEs), this paper studies dynamic convex risk measures for risky positions in a simple discrete-time, binomial tree model. A relationship between BSDEs and dynamic convex risk measures is developed using nonlinear expectations. The time consistency of dynamic convex risk measures is discussed in the binomial tree framework. A relationship between prices and risks is also established. Two particular cases of dynamic convex risk measures, namely risk measures with stochastic distortions and entropic risk measures, and their mathematical properties are discussed.
- ItemOpen AccessBond valuation under a discrete-time regime-switching term-structure model and its continuous-time extension(Emerald, 2011) Elliott, Robert; Siu, Tak Kuen; Badescu, AlexPurpose – The purpose of this paper is to consider a discrete-time, Markov, regime-switching, affine term-structure model for valuing bonds and other interest rate securities. The proposed model incorporates the impact of structural changes in (macro)-economic conditions on interest-rate dynamics. The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account. Design/methodology/approach – The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account. Findings – The authors derive a simple way to give exponential affine forms of bond prices using backward induction. The authors also consider a continuous-time extension of the model and derive exponential affine forms of bond prices using the concept of stochastic flows.
- ItemOpen AccessA BSDE approach to a risk-based optimal investment of an insurer(Elsevier, 2011) Elliott, Robert; Siu, Tak KuenWe discuss a backward stochastic differential equation, (BSDE), approach to a risk-based, optimal investment problem of an insurer. A simplified continuous-time economy with two investment vehicles, namely, a fixed interest security and a share, is considered. The insurer’s risk process is modeled by a diffusion approximation to a compound Poisson risk process. The goal of the insurer is to select an optimal portfolio so as to minimize the risk described by a convex risk measure of his/her terminal wealth. The optimal investment problem is then formulated as a zero-sum stochastic differential game between the insurer and the market. The BSDE approach is used to solve the game problem. It leads to a simple and natural approach for the existence and uniqueness of an optimal strategy of the game problem without Markov assumptions. Closed-form solutions to the optimal strategies of the insurer and the market are obtained in some particular cases.
- ItemOpen AccessCharacteristic functions and option valuation in a Markov chain market(Elsevier, 2011) Elliott, Robert; Liew, Chuin Ching; Siu, Tak KuenWe introduce an approach for valuing some path-dependent options in a discrete-time Markov chain market based on the characteristic function of a vector of occupation times of the chain. A pricing kernel is introduced and analytical formulas for the prices of Asian options and occupation time call options are derived.
- ItemOpen AccessControl of discrete-time HMM partially observed under fractional Gaussian noises(Elsevier, 2011) Elliott, Robert; Siu, Tak KuenA discrete-time control problem of a finite-state hidden Markov chain partially observed in a fractional Gaussian process is discussed using filtering. The control problem is then recast as a separated problem with information variables given by the unnormalized conditional probabilities of the whole path of the hidden Markov chain. A dynamic programming result and a minimum principle are obtained.
- ItemOpen AccessOn filtering and estimation of a threshold stochastic volatility model(Elsevier, 2011) Elliott, Robert; Liew, Chuin Ching; Siu, Tak KuenWe derive a nonlinear filter and the corresponding filter-based estimates for a threshold autoregressive stochastic volatility (TARSV) model. Using the technique of a reference probability measure, we derive a nonlinear filter for the hidden volatility and related quantities. The filter-based estimates for the unknown parameters are then obtained from the EM algorithm.
- ItemOpen AccessOn pricing and hedging options in regime-switching models with feedback effect(Elsevier, 2011) Elliott, Robert; Siu, Tak Kuen; Badescu, AlexandruWe study the pricing and hedging of European-style derivative securities in a Markov, regime-switching, model with a feedback e ect depending on the economic condition. We adopt a pricing kernel which prices both nancial and economic risks explicitly in a dynamically incomplete market and we provide an equilibrium analysis. A martingale representation for a European-style index option's price is established based on the price kernel. The martingale representation is then used to construct the local risk-minimizing strategy explicitly and to characterize the corresponding pricing measure.
- ItemOpen AccessUtility-based indifference pricing in regime-switching models(Elsevier, 2011) Elliott, Robert; Siu, Tak KuenIn this paper, we study utility-based indifference pricing and hedging of a contingent claim in a continuous-time, Markov, regime-switching model. The market in this model is incomplete, so there is more than one price kernel. We specify the parametric form of price kernels so that both market risk and economic risk are taken into account. The pricing and hedging problem is formulated as a stochastic optimal control problem and is discussed using the dynamic programming approach. A verification theorem for the Hamilton–Jacobi–Bellman (HJB) solution to the problem is given. An issuer’s price kernel is obtained from a solution of a system of linear programming problems and an optimal hedged portfolio is determined.