Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets

We consider a robust consumption‐investment problem under constant relative risk aversion and constant absolute risk aversion utilities. The time‐varying confidence sets are specified by Θ, a correspondence from [0, T] to the space of the Lévy triplets, and describe a priori drift, volatility, and jump information. For each possible measure, the log‐price processes of stocks are semimartingales, and the triplet of their differential characteristics is almost surely a measurable selector from the correspondence Θ. By proposing and investigating the global kernel, an optimal policy and a worst‐case measure are generated from a saddle point of the global kernel, and they constitute a saddle point of the objective function.     

Value of hedge and expected returns

We demonstrate how it is possible to generate value for an investor with a hedge attached to the buy-and-hold strategy of an S&P 500 index fund. We study the S&P 500 index portfolio (not including dividends) and the value-weighted S&P 500 index portfolio (including dividends) of the Center for Research in Securities Prices for 1967:01–2011:12, using the capacity utilization and the unemployment rates in real time to determine if a hedge position should be initiated or closed. A hedge is initiated if the capacity utilization, the unemployment rate or a combination of the two signals a contraction in the real economy. The hedge position is closed if it signals otherwise an expansion. We use utility gains (Campbell and Thompson 2008), the manipulation-proof performance measure (MPPM) statistics (Ingersoll et al. 2007) and the P-Sharpe ratio (Bailey and López de Prado 2012) to evaluate the performance of a particular hedge strategy. The empirical results show that there are infinitely many hedges that can generate positive utility gains, higher MPPM statistics and higher P-Sharpe ratios.     

ARBITRAGE‐FREE BILATERAL COUNTERPARTY RISK VALUATION UNDER COLLATERALIZATION AND APPLICATION TO CREDIT DEFAULT SWAPS

We develop an arbitrage‐free valuation framework for bilateral counterparty risk, where collateral is included with possible rehypothecation. We show that the adjustment is given by the sum of two option payoff terms, where each term depends on the netted exposure, i.e., the difference between the on‐default exposure and the predefault collateral account. We then specialize our analysis to credit default swaps (CDS) as underlying portfolios, and construct a numerical scheme to evaluate the adjustment under a doubly stochastic default framework. In particular, we show that for CDS contracts a perfect collateralization cannot be achieved, even under continuous collateralization, if the reference entity’s and counterparty’s default times are dependent. The impact of rehypothecation, collateral margining frequency, and default correlation‐induced contagion is illustrated with numerical examples.     

How risky is a random process?

The riskiness of random processes is compared by (a) employing a decision theoretic equivalence between processes and lotteries on path-spaces to identify the riskiness of the former with that of the latter, and (b) using the theory of comparative riskiness of lotteries over vector spaces to compare the riskiness of lotteries on a given path-space. We derive the equivalence used in step (a) and contribute a new criterion to the theory applied in step (b). The validity of the new criterion, which applies second order stochastic dominance to utility distributions, is established by showing its equivalence to the benchmark decision theoretic criterion when comparing the riskiness of lotteries over any vector space. We demonstrate the theory’s tractability via diverse economic applications.     

Life-cycle funds: Much Ado about Nothing?

The core idea of life-cycle funds or target-date funds is to decrease the fund's equity exposure and conversely increase its bond exposure towards the fund's target date. Such funds have been gaining significant market share and were recently set as default choice of asset allocation in numerous defined contribution schemes or related old-age provision products in several countries. Hence, an assessment of life-cycle funds’ risk-return profiles – that is, the probability distribution of returns – is essential for sustainable financial planning of a large group of investors. This paper studies the risk-return profile of life-cycle funds in particular compared to simple balanced or lifestyle funds that apply a constant equity portion throughout the fund's term instead. In a Black–Scholes model, we derive balanced funds that reproduce the risk-return profile of an arbitrary life-cycle fund for single and regular contributions. We then analyze the accuracy of our results under more complex asset models with stochastic interest rates, stochastic equity volatility and jumps. We further show that frequently used ‘rule of thumb approximations’ that only take into account the life-cycle fund's average equity portion are not suitable to approximate a life-cycle fund's risk-return profile. Our results on the one hand facilitate sustainable financial planning and on the other hand challenge the very existence of life-cycle funds since appropriately calibrated balanced funds can offer a similar (often dominating) risk-return profile.     

VALUATION OF BARRIER OPTIONS VIA A GENERAL SELF‐DUALITY

Classical put–call symmetry relates the price of puts and calls under a suitable dual market transform. One well‐known application is the semistatic hedging of path‐dependent barrier options with European options. This, however, in its classical form requires the price process to observe rather stringent and unrealistic symmetry properties. In this paper, we develop a general self‐duality theorem to develop valuation schemes for barrier options in stochastic volatility models with correlation.     

Optimal transit fare and service frequency of a nonlinear origin-destination based fare structure

This paper proposes a new nonlinear distance-based transit fare structure, which is measured by a function of the Euclidean distance between the origin and destination stations, termed as Origin-Destination (OD)-based fare. The novel fare structure encourages passengers to freely choose the most efficient trip plan. An optimization model is formulated based on a three-party game (involving the transport authority, transit company, and passenger) to determine the optimal fare function and frequency. An artificial bee colony algorithm is adopted to solve the model. Finally, a numerical example is provided to verify the proposed method.     

Optimal investment-consumption-insurance with random parameters

This paper discusses an optimal investment, consumption, and life insurance purchase problem for a wage earner in a complete market with Brownian information. Specifically, we assume that the parameters governing the market model and the wage earner, including the interest rate, appreciation rate, volatility, force of mortality, premium-insurance ratio, income and discount rate, are all random processes adapted to the Brownian motion filtration. Our modeling framework is very general, which allows these random parameters to be unbounded, non-Markovian functionals of the underlying Brownian motion. Suppose that the wage earner’s preference is described by a power utility. The wage earner’s problem is then to choose an optimal investment-consumption-insurance strategy so as to maximize the expected, discounted utilities from intertemporal consumption, legacy and terminal wealth over an uncertain lifetime horizon. We use a novel approach, which combines the Hamilton–Jacobi–Bellman equation and backward stochastic differential equation (BSDE) to solve this problem. In general, we give explicit expressions for the optimal investment-consumption-insurance strategy and the value function in terms of the solutions to two BSDEs. To illustrate our results, we provide closed-form solutions to the problem with stochastic income, stochastic mortality, and stochastic appreciation rate, respectively.     

Impact of quality on estimations of hotel efficiency

This paper provides empirical evidence on the impact of output quality on hotel efficiency. It demonstrates how ignoring quality can lead to erroneous efficiency estimates. The study uses stochastic frontier methodology and the model proposed by Battese and Coelli (1995) to estimate the efficiency of 838 hotels in Spain in the period 2009–2013. The key advantage of this methodology is its ability to estimate efficiency and identify factors that explain differences in efficiency in a single-stage sampling procedure. Estimates of cost efficiency, which only include the costs of higher quality, are compared to those of profit efficiency, which not only consider costs but also the revenues generated by higher quality. Results show that quality has a negative impact on cost efficiency and a positive one on profit efficiency. Thus, hotel management should implement strategies that increase the value of their services as a way to achieve sustainable competitive advantages.     

跳跃随机波动的阈值模型风险值的贝叶斯估计

文章基于一类跳跃随机波动的阈值模型风险值估计贝叶斯分析,在给定先验分布下,以马尔科夫链蒙特卡洛方法估计模型中的未知参数,并给出了MCMC模拟算法,进而讨论了风险值的预测。根据模拟结果,我们得知,如果没有考虑金融时间序列的外生冲击导致的跳跃行为,将会高估风险值,因此考虑跳跃行为后,将增加风险值估计的精度。