Coherent risk measures for derivatives under Black-Scholes Economy

This paper proposes a risk measure for a portfolio of European-style derivative securities over a fixed time horizon under the Black–Scholes economy. The proposed risk measure is scenario-based along the same line as [3]. The risk measure is constructed by using the risk-neutral probability (-measure), the physical probability (-measure) and a family of subjective probability measures. The subjective probabilities are introduced by using Girsanov's theorem. In this way, we provide risk managers or regulators with the flexibility of adjusting the risk measure according to their risk preferences and subjective beliefs. The advantages of the proposed measure are that it is easy to implement and that it satisfies the four desirable properties introduced in [3], which make it a coherent risk measure. Finally, we incorporate the presence of transaction costs into our framework.postprin

Pricing exotic options under a high-order markovian regime switching model

We consider the pricing of exotic options when the price dynamics of the underlying risky asset are governed by a discrete-time Markovian regime-switching process driven by an observable, high-order Markov model (HOMM). We assume that the market interest rate, the drift, and the volatility of the underlying risky asset's return switch over time according to the states of the HOMM, which are interpreted as the states of an economy. We will then employ the well-known tool in actuarial science, namely, the Esscher transform to determine an equivalent martingale measure for option valuation. Moreover, we will also investigate the impact of the high-order effect of the states of the economy on the prices of some path-dependent exotic options, such as Asian options, lookback options, and barrier options.published_or_final_versio

Optimal dividends with debts and nonlinear insurance risk processes

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On infectious models for dependent default risk

Modeling dependent defaults is a key issue in risk measurement and management. In this paper, we introduce a Markovian infectious model to describe the dependent relationship of default processes of credit entities. The key idea of the proposed model is based on the concept of common shocks adopted in the insurance industry. We compare the proposed model to both one-sector and two-sector models considered in the credit literature using real default data. A log-likelihood ratio test is applied to compare the goodness-of- fit of the proposed model. Our empirical results reveal that the proposed model outperforms both the one-sector and two-sector models. © 2011 IEEE.published_or_final_versionThe 4th International Joint Conference on Computational Sciences and Optimization (CSO 2011), Yunnan, China, 15-19 April 2011. In Proceedings of the 4th CSO, 2011, p. 1196-120

Optimal submission problem in a limit order book with VaR constraints

We consider an optimal selection problem for bid and ask quotes subject to a value-at-Risk (VaR) constraint when arrivals of the buy and sell orders are governed by a Poisson process. The problem is formulated as a constrained utility maximization problem over a finite time horizon. Using a diffusion approximation to Poisson arrivals of market orders, the dynamic programming principle can be applied here. We propose an efficient procedure to solve this constrained utility maximization problem based on a successive approximation algorithm. Numerical examples with and without the VaR constraint are used to illustrate the effect of the risk constraint on the dealer's choices. We also conduct numerical experiments to analyze the impacts of the risk constraint on dealer's terminal profit. © 2012 IEEE.published_or_final_versionThe 5th International Joint Conference on Computational Sciences and Optimization (CSO 2012), Harbin, Heilongjiang Province, China, 23-26 June 2012. In Proceedings of the 5th CSO, 2012, p. 266-27

Asset allocation under regime-switching models

We discuss an optimal asset allocation problem in a wide class of discrete-time regime-switching models including the hidden Markovian regime-switching (HMRS) model, the interactive hidden Markovian regime-switching (IHMRS) model and the self-exciting threshold autoregressive (SETAR) model. In the optimal asset allocation problem, the object of the investor is to select an optimal portfolio strategy so as to maximize the expected utility of wealth over a finite investment horizon. We solve the optimal portfolio problem using a dynamic programming approach in a discrete-time set up. Numerical results are provided to illustrate the practical implementation of the models and the impacts of different types of regime switching on optimal portfolio strategies. © 2012 IEEE.published_or_final_versio

Optimal insurance risk control with multiple reinsurers

An optimal insurance risk control problem is discussed in a general situation where several reinsurance companies enter into a reinsurance treaty with an insurance company. These reinsurance companies adopt variance premium principles with different parameters. Dividends with fixed costs and taxes are paid to shareholders of the insurance company. Under certain conditions, a combined proportional reinsurance treaty is shown to be optimal in a class of plausible reinsurance treaties. Within the class of combined proportional reinsurance strategies, analytical expressions for the value function and the optimal strategies are obtained.postprin

Reliable tracking algorithm for multiple reference frame motion estimation

2011-2012 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe