Risk minimizing hedging for a partially observed high frequency data model

Risk-minimizing hedging strategies for contingent claims are studied in a general model for intraday stock price movements in the case of partial information. The dynamics of the risky asset price is described throught a marked point process Y, whose local characteristics depend on some unobservable hidden state variable X. In the model presented the processes Y and X may have common jump times, which means that the trading activity may affect the law of X and could be also related to the presence of catastrophic events. The hedger is restricted to observing past asset prices. Thus, we are in presence not only of an incomplete market situation but also of partial information. Considering the case where the price of the risky asset is modeled directly under a martingale measure, the computation of the risk-minimizing hedging strategy under this partial information is obtained by using a projection result (M. Schweizer, Risk minimizing hedging strategies under restricted information, Mathematical Finance 4 (1994) 327–342). This approach leads to a filtering problem with marked point process observations whose solution, obtained via the Kushner-Stratonovich equation, allows us to provide a complete solution to the heding problem.     

On the construction of nearly optimal strategies for a general problem of control of partially observed diffusions

In the paper a stochastic control problem consisting of continuously acting controls, impulse controls and stopping times of a partially observed diffusion with discounted cost functional is considered. The problem is successively approximated by time, observation, control and space discretizations to obtain finally a completely observed finite valued control problem. It is shown that the optimal strategy for the approximating problem, which can be numerically computed, is nearly optimal for the original problem     

Mean‐Reverting Market Model: Speculative Opportunities and Non‐Arbitrage

The paper studies arbitrage opportunities and possible speculative opportunities for diffusion mean‐reverting market models. It is shown that the Novikov condition is satisfied for any time interval and for any set of parameters. It is non‐trivial because the appreciation rate has Gaussian distribution converging to a stationary limit. It follows that the mean‐reverting model is arbitrage‐free for any finite time interval. Further, it is shown that this model still allows some speculative opportunities: a gain for a wide enough set of expected utilities can be achieved for a strategy that does not require any hypothesis on market parameters and does not use estimation of these parameters.     

On the accuracy of a nonlinear finite volume method for the solution of diffusion problems using different interpolations strategies

In this paper, we consider a nonlinear finite volume method to solve the steady‐state diffusion equation in nonhomogeneous and non‐isotropic media. The method is nonlinear even if the original problem is linear. In its original form, the scheme is monotone, because the coefficient matrix is monotone under certain assumptions and, as a consequence, whenever the analytic operator demands, it preserves the positivity of numerical solutions. On the other hand, the scheme is unable to reproduce piecewise linear solutions exactly. In order to recover this interesting feature, we use two different interpolation strategies. In this case, even though we are unable to prove monotonicity, we show some numerical evidences that the combined method has an improved behavior, producing second order accurate solutions, even for nonhomogeneous and strongly anisotropic media. Copyright © 2013 John Wiley & Sons, Ltd.     

Chiral separability of boron cluster species studied by screening approaches utilizing polysaccharide‐based chiral stationary phases

In this study, the screening steps of chiral separation strategies with polysaccharide‐based chiral stationary phases were applied on boron cluster compounds in normal‐phase liquid chromatography (NPLC) and polar organic solvents chromatography (POSC). Since the screening steps were initially developed to analyze organic compounds, their applicability for boron clusters was investigated. Overall, the screening steps in NPLC were applicable for the separation of zwitterions, while for anions mostly no elution was observed. A hypothesis for the latter behavior is precipitation of anions in the nonpolar mobile phases. Ten out of 11 compounds could be partially or baseline separated on the NPLC screening systems. In POSC, all zwitterions were separated on at least one of the screening systems, with an overall lower retention as in NPLC. Anions were detected but not separated in the majority of the experiments. Also their retention on the chiral stationary phases was very limited. This study showed that the chiral discrimination potential of chemically modified polysaccharides is meaningful for chiral separations of structurally chiral boron cluster species, but needs further systematic research, in which recognition mechanisms should be further explored. In addition, some unusual peaks also indicated that conditions with a high separation efficiency must first be searched for some of the tested systems. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal strategies for asset allocation and consumption under stochastic volatility

Selecting optimal asset allocation and consumption strategies is an important, but difficult, topic in modern finance. The dynamics is governed by a nonlinear partial differential equation. Stochastic volatility adds further complication. Even to obtain a numerical solution is challenging. Here, we develop a closed-form approximate solution. We show that our theoretical predictions for the optimal asset allocation strategy and the optimal consumption strategy are in surprisingly good agreement with the results from full numerical computations.     

Improved Deep Q-Network for User-Side Battery Energy Storage Charging and Discharging Strategy in Industrial Parks

Battery energy storage technology is an important part of the industrial parks to ensure the stable power supply, and its rough charging and discharging mode is difficult to meet the application requirements of energy saving, emission reduction, cost reduction, and efficiency increase. As a classic method of deep reinforcement learning, the deep Q-network is widely used to solve the problem of user-side battery energy storage charging and discharging. In some scenarios, its performance has reached the level of human expert. However, the updating of storage priority in experience memory often lags behind updating of Q-network parameters. In response to the need for lean management of battery charging and discharging, this paper proposes an improved deep Q-network to update the priority of sequence samples and the training performance of deep neural network, which reduces the cost of charging and discharging action and energy consumption in the park. The proposed method considers factors such as real-time electricity price, battery status, and time. The energy consumption state, charging and discharging behavior, reward function, and neural network structure are designed to meet the flexible scheduling of charging and discharging strategies, and can finally realize the optimization of battery energy storage benefits. The proposed method can solve the problem of priority update lag, and improve the utilization efficiency and learning performance of the experience pool samples. The paper selects electricity price data from the United States and some regions of China for simulation experiments. Experimental results show that compared with the traditional algorithm, the proposed approach can achieve better performance in both electricity price systems, thereby greatly reducing the cost of battery energy storage and providing a stronger guarantee for the safe and stable operation of battery energy storage systems in industrial parks.     

基于Tikhonov正则参量后验选择策略的PCS颗粒粒度反演方法

采用基于Morozov偏差原理的后验策略来选择最优正则参量,并采用此方法对单峰和多峰分布颗粒系的模拟电场自相关函数进行了反演,结果表明,对于单峰颗粒体系,当电场自相关函数的扰动误差小于0.05时,反演得到的峰值准确,当电场自相关函数的扰动误差大于0.05时,反演得到的峰值偏离所模拟的颗粒粒径.正则参量初始值在0.000 02～2范围内,在反演所得的峰值准确的基础上,正则参量初始值越小,反演得到的分布宽度越窄.收敛误差在0.000 05～50范围内,在保持反演结果稳定的基础上,收敛误差取值越大,反演得到的分布宽度越窄.对于多峰颗粒体系,当颗粒系中的颗粒粒径差别较小时,峰值向平均值偏移,当颗粒系中的颗粒粒径差别较大时,小颗粒粒径分布以噪音的形式出现.     

Zero-Sum Ergodic Semi-Markov Games with Weakly Continuous Transition Probabilities

Zero-sum ergodic semi-Markov games with weakly continuous transition probabilities and lower semicontinuous, possibly unbounded, payoff functions are studied. Two payoff criteria are considered: the ratio average and the time average. The main result concerns the existence of a lower semicontinuous solution to the optimality equation and its proof is based on a fixed-point argument. Moreover, it is shown that the ratio average as well as the time average payoff stochastic games have the same value. In addition, one player possesses an ε-optimal stationary strategy (ε>0), whereas the other has an optimal stationary strategy. A. Jaśkiewicz is on leave from Institute of Mathematics and Computer Science, Wrocław University of Technology. This work is supported by MNiSW Grant 1 P03A 01030.     

A mathematical model for the first-pass dynamics of antibiotics acting on the cardiovascular system

We present a preliminary first-pass dynamic model for delivery of drug compounds to the lungs and heart. We use a compartmental mass-balance approach to develop a system of nonlinear differential equations for mass accumulated in the heart as a result of intravenous injection. We discuss sensitivity analysis as well as methodology for minimizing mass in the heart while maximizing mass delivered to the lungs on a first circulatory pass.