Continuous-time mean-variance efficiency: the 80% rule

This paper studies a continuous-time market where an agent, having specified an investment horizon and a targeted terminal mean return, seeks to minimize the variance of the return. The optimal portfolio of such a problem is called mean-variance efficient \`{a} la Markowitz. It is shown that, when the market coefficients are deterministic functions of time, a mean-variance efficient portfolio realizes the (discounted) targeted return on or before the terminal date with a probability greater than 0.8072. This number is universal irrespective of the market parameters, the targeted return and the length of the investment horizon.Comment: Published at http://dx.doi.org/10.1214/105051606000000349 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimal stopping under probability distortion

We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We develop a new approach, based on a reformulation of the problem where one optimally chooses the probability distribution or quantile function of the stopped state. An optimal stopping time can then be recovered from the obtained distribution/quantile function, either in a straightforward way for several important cases or in general via the Skorokhod embedding. This approach enables us to solve the problem in a fairly general manner with different shapes of the payoff and probability distortion functions. We also discuss economical interpretations of the results. In particular, we justify several liquidation strategies widely adopted in stock trading, including those of "buy and hold", "cut loss or take profit", "cut loss and let profit run" and "sell on a percentage of historical high".Comment: Published in at http://dx.doi.org/10.1214/11-AAP838 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Informed and Uniformed Agent's Price of a Contingent Claim

The existence of an adapted solution to a backward stochastic differential equation which is not adapted to the filtration of the underlying Brownian motion is proved. This result is applied to the pricing of contingent claims. It allows to compare the prices of agents who have different information about the evolution of the market. The problem is considered in both the classical and the Föllmer-Schweizer hedging case.

Interplay between dividend rate and business constraints for a financial corporation

We study a model of a corporation which has the possibility to choose various production/business policies with different expected profits and risks. In the model there are restrictions on the dividend distribution rates as well as restrictions on the risk the company can undertake. The objective is to maximize the expected present value of the total dividend distributions. We outline the corresponding Hamilton-Jacobi-Bellman equation, compute explicitly the optimal return function and determine the optimal policy. As a consequence of these results, the way the dividend rate and business constraints affect the optimal policy is revealed. In particular, we show that under certain relationships between the constraints and the exogenous parameters of the random processes that govern the returns, some business activities might be redundant, that is, under the optimal policy they will never be used in any scenario.Comment: Published at http://dx.doi.org/10.1214/105051604000000909 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Wireless Information and Power Transfer: Architecture Design and Rate-Energy Tradeoff

Simultaneous information and power transfer over the wireless channels potentially offers great convenience to mobile users. Yet practical receiver designs impose technical constraints on its hardware realization, as practical circuits for harvesting energy from radio signals are not yet able to decode the carried information directly. To make theoretical progress, we propose a general receiver operation, namely, dynamic power splitting (DPS), which splits the received signal with adjustable power ratio for energy harvesting and information decoding, separately. Three special cases of DPS, namely, time switching (TS), static power splitting (SPS) and on-off power splitting (OPS) are investigated. The TS and SPS schemes can be treated as special cases of OPS. Moreover, we propose two types of practical receiver architectures, namely, separated versus integrated information and energy receivers. The integrated receiver integrates the front-end components of the separated receiver, thus achieving a smaller form factor. The rate-energy tradeoff for the two architectures are characterized by a so-called rate-energy (R-E) region. The optimal transmission strategy is derived to achieve different rate-energy tradeoffs. With receiver circuit power consumption taken into account, it is shown that the OPS scheme is optimal for both receivers. For the ideal case when the receiver circuit does not consume power, the SPS scheme is optimal for both receivers. In addition, we study the performance for the two types of receivers under a realistic system setup that employs practical modulation. Our results provide useful insights to the optimal practical receiver design for simultaneous wireless information and power transfer (SWIPT).Comment: to appear in IEEE Transactions on Communication

Collaborating and Conflicted: Being Jewish in Secular and Multicultural Hong Kong

This essay looks into the conflicts and collaborations amongst different Jewish groups in Hong Kong from the second half of the nineteenth century to the years following Hong Kong?s handover to the People?s Republic of China (PRC) in 1997. In examining this former British Colony, now a Special Administrative Region (SAR) of People?s Republic of China, this essay adds a new dimension to the parallel discussions of intra-communal Jewish life in Europe and North Americ