Dr Boda Kang

Filar, J. & Kang, B. 2006, 'Two Types of Risk' in Yan, H; Yin, G; Zhang, Q. (eds), Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queue, Springer, Germany, pp. 109-140.
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The risk encountered in many environmental problems appears to exhibit special +two-sided+ characteristics. For instance, in a given area and in a given period, farmers do not want to see too much or too little rainfall. They hope for rainfall that is in some given interval. We formulate and solve this problem with the help of a +two-sided loss function+ that depends on the above range. Even in financial portfolio optimization a loss and a gain are +two sides of a coin+, so it is desirable to deal with them in a manner that reflects an investor+s relative concern. Consequently, in this paper, we define Type I risk: +the loss is too big+ and Type II risk: +the gain is too small+. Ideally, we would want to minimize the two risks simultaneously. However, this may be impossible and hence we try to balance these two kinds of risk. Namely, we tolerate certain amount of one risk when minimizing the other. The latter problem is formulated as a suitable optimization problem and illustrated with a numerical example.

Chiarella, C., Kang, B. & Meyer, G. 2012, 'The evaluation of barrier option prices under stochastic volatility', Computers & Mathematics With Applications, vol. 64, no. 6, pp. 2034-2048.
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This paper considers the problem of numerically evaluating barrier option prices when the dynamics of the underlying are driven by stochastic volatility following the square root process of Heston (1993)[7]. We develop a method of lines approach to evaluate the price as well as the delta and gamma of the option. The method is able to efficiently handle both continuously monitored and discretely monitored barrier options and can also handle barrier options with early exercise features. In the latter case, we can calculate the early exercise boundary of an American barrier option in both the continuously and discretely monitored cases.

Chiarella, C., Kang, B., Meyer, G. & Ziogas, A. 2009, 'The evaluation of American option prices under stochastic volatility and jump diffusion dynamics using the method of lines', International Journal of Theoretical and Applied Finance, vol. 12, no. 3, pp. 393-425.
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This paper considers the problem of numerically evaluating American option prices when the dynamics of the underlying are driven by both stochastic volatility following the square root process of Heston [18], and by a Poisson jump process of the type originally introduced by Merton [25]. We develop a method of lines algorithm to evaluate the price as well as the delta and gamma of the option, thereby extending the method developed by Meyer [26] for the case of jump-diffusion dynamics. The accuracy of the method is tested against two numerical methods that directly solve the integro-partial differential pricing equation. The first is an extension to the jump-diffusion situation of the componentwise splitting method of Ikonen and Toivanen [21]. The second method is a Crank-Nicolson scheme that is solved using projected successive over relaxation and which is taken as the benchmark for the price. The relative efficiency of these methods for computing the American call option price, delta, gamma and free boundary is analysed. If one seeks an algorithm that gives not only the price but also the delta and gamma to the same level of accuracy for a given computational effort then the method of lines seems to perform best amongst the methods considered.

Kang, B. & Filar, J. 2006, 'Time consistent dynamic risk measures', Mathematical Methods of Operations Research, vol. 63, no. 1, pp. 169-186.
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We introduce the time-consistency concept that is inspired by the so-called +principle of optimality+ of dynamic programming and demonstrate + via an example + that the conditional value-at-risk (CVaR) need not be time-consistent in a multi-stage case. Then, we give the formulation of the target-percentile risk measure which is time-consistent and hence more suitable in the multi-stage investment context. Finally, we also generalize the value-at-risk and CVaR to multi-stage risk measures based on the theory and structure of the target-percentile risk measure.

Kang, B., Filar, J., Lin, Y. & Spanjers, L. 2004, 'Stochastic Target Hitting Time and the Problem of Early Retirement', IEEE Transactions On Automatic Control, vol. 49, no. 3, pp. 409-419.
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We consider a problem of optimal control of a +retirement investment fund+ over a finite time horizon with a target hitting time criteria. That is, we wish to decide, at each stage, what percentage of the current retirement fund to allocate into the limited number of investment options so that a decision maker can maximize the probability that his or her wealth exceeds a target prior to his or her retirement. We use Markov decision processes with probability criteria to model this problem and give an example based on data from certain options available in an Australian retirement fund.

Lin, Y., Wu, C. & Kang, B. 2003, 'Optimal Models with Maximizing the Probability of First Achieving Target Value in the Preceding Stages', Science In China Series A, vol. 46, no. 3, pp. 396-414.
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Decision makers often face the need of performance guarantee with some sufficiently high probability. Such problems can be modelled using a discrete time Markov decision process (MDP) with a probability criterion for the first achieving target value. The objective is to find a policy that maximizes the probability of the total discounted reward exceeding a target value in the preceding stages. We show that our formulation cannot be described by former models with standard criteria. We provide the properties of the objective functions, optimal value functions and optimal policies. An algorithm for computing the optimal policies for the finite horizon case is given. In this stochastic stopping model, we prove that there exists an optimal deterministic and stationary policy and the optimality equation has a unique solution. Using perturbation analysis, we approximate general models and prove the existence of ?-optimal policy for finite state space. We give an example for the reliability of the satellite systems using the above theory. Finally, we extend these results to more general cases.

Lin, Y., Kang, B. & Wu, C. 2001, 'Finite horizon markov decision minimizing risk Models in borel state space', Chinese Sciences Abstract Series A, vol. ?, pp. 1273-1278.

Lin, Y., Wu, C. & Kang, B. 2001, 'Markov decision minimizing risk models for the first achieving target value', Chinese Sciences Abstract Series A, vol. ?, pp. 1269-1273.

Chiarella, C., Clewlow, L. & Kang, B. 2012, 'The evaluation of gas swing contracts with regime switching', Numerical Methods for Finance Conference 2011, Limerick, Ireland, June 2011 in Topics in Numerical Methods for Finance: Proceedings in Mathematics and Statistics, ed Mark Cummins, Finbar Murphy and John J. H. Miller, Springer, Germany, pp. 155-176.
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