Trading to Stops

The use of trading stops is a common practice in financial markets for a variety of reasons: it reduces the frequency of trading and thereby transaction costs; it provides a simple way to control losses on a given trade, while also ensuring that profit-taking is not deferred indefinitely; and it allows opportunities to consider reallocating resources to other investments. In this paper, we try to explain why the use of stops may be desirable, by proposing a simple objective to be optimized. We investigate a number of commonly used rules for the placing and use of stops, either fixed or moving, with fixed costs, showing how to identify optimal levels at which to set stops, and compare the performance of different rules and strategies.This is the final published version of the paper. First Published in Siam Journal on Financial Mathematics in 2014, published by the Society of Industrial and Applied Mathematics (SIAM). Copyright © by SIAM. Unauthorized reproduction of this article is prohibited

Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis

In this paper, we consider an optimal reinsurance problem to minimize the probability of drawdown for the scaled Cram´er-Lundberg risk model when the reinsurance premium is computed according to the mean-variance premium principle. We extend the work of Liang et al. [16] to the case of minimizing the probability of drawdown. By using the comparison method and the tool of adjustment coefficients, we show that the minimum probability of drawdown for the scaled classical risk model converges to the minimum probability for its diffusion approximation, and the rate of convergence is of order O(n−1/2). We further show that using the optimal strategy from the diffusion approximation in the scaled classical risk model is O(n−1/2)-optimalEste documento es una versión del artículo publicado en SIAM Journal on Financial Mathematics, 14(1), 279–313Universidad Torcuato Di TellaHebei University of TechnologyDepartment of Mathematics, University of Michiga

Weak Markovian Approximations of Rough Heston

The rough Heston model is a very popular recent model in mathematical finance; however, the lack of Markov and semimartingale properties poses significant challenges in both theory and practice. A way to resolve this problem is to use Markovian approximations of the model. Several previous works have shown that these approximations can be very accurate even when the number of additional factors is very low. Existing error analysis is largely based on the strong error, corresponding to the $L^2$ distance between the kernels. Extending earlier results by [Abi Jaber and El Euch, SIAM Journal on Financial Mathematics 10(2):309--349, 2019], we show that the weak error of the Markovian approximations can be bounded using the $L^1$-error in the kernel approximation for general classes of payoff functions for European style options. Moreover, we give specific Markovian approximations which converge super-polynomially in the number of dimensions, and illustrate their numerical superiority in option pricing compared to previously existing approximations. The new approximations also work for the hyper-rough case $H > -1/2$

Horizon-unbiased Investment with Ambiguity

In the presence of ambiguity on the driving force of market randomness, we consider the dynamic portfolio choice without any predetermined investment horizon. The investment criteria is formulated as a robust forward performance process, reflecting an investor's dynamic preference. We show that the market risk premium and the utility risk premium jointly determine the investors' trading direction and the worst-case scenarios of the risky asset's mean return and volatility. The closed-form formulas for the optimal investment strategies are given in the special settings of the CRRA preference