Risk management in liner ship fleet deployment: A joint chance constrained programming model

This paper provides a tangible methodology to deal with the liner ship fleet deployment problem aiming at minimizing the total cost while maintaining a service level under uncertain container demand. The problem is first formulated as a joint chance constrained programming model, and the sample average approximation method and mixed-integer programming are used to deal with it. Finally, a numerical example of a liner shipping network is carried out to verify the applicability of the proposed model and solution algorithm. It is found that the service level has significant effect on the total cost.     

A saddlepoint approximation to the distribution of the sum of independent non‐identically beta random variables

The exact distribution of the sum of more than two independent beta random variables has not been known. Even in terms of approximations, only the normal approximation is known for the sum. Motivated by Murakami [Statistica Neerlandica, 2014, doi:10.1111/stan.12032], we derive here a saddlepoint approximation for the distribution of sum. An extensive simulation study shows that it always performs better than the normal approximation.     

Estimating stochastic volatility models using integrated nested Laplace approximations

Volatility in financial time series is mainly analysed through two classes of models; the generalized autoregressive conditional heteroscedasticity (GARCH) models and the stochastic volatility (SV) ones. GARCH models are straightforward to estimate using maximum-likelihood techniques, while SV models require more complex inferential and computational tools, such as Markov Chain Monte Carlo (MCMC). Hence, although provided with a series of theoretical advantages, SV models are in practice much less popular than GARCH ones. In this paper, we solve the problem of inference for some SV models by applying a new inferential tool, integrated nested Laplace approximations (INLAs). INLA substitutes MCMC simulations with accurate deterministic approximations, making a full Bayesian analysis of many kinds of SV models extremely fast and accurate. Our hope is that the use of INLA will help SV models to become more appealing to the financial industry, where, due to their complexity, they are rarely used in practice.     

Multilinear approximation on rectangles and the related moment problem

The Edmundson–Madansky (E–M) inequality provides an upper bound of the expectation of a convex function of a random vector, provided the components of the random vector are stochastically independent. Frauendorfer and Kall extended the E–M inequality to the dependent case. This paper provides the natural algebraic setting for this extension. It is shown that multilinear approximation is the basic idea. The results and the calculations are simplified considerably by the use of Kronecker products. Moreover, the class of all functions for which the general E–M bound holds is characterized completely. It includes many nonconvex functions, for instance the multi-chord-dominated functions, which include the multiconvex functions.     

规则RA码在混合信道上的高斯估计

将高斯估计方法运用到规则重复累积（RA）码在具有加性白色高斯噪声和删除干扰的混合信道上的性能分析中．导出了RA码在该信道上概率密度进化的递归等式和误码率的解析表达式。仿真结果验证了解析结果的正确性。因此解析结果可以直接用来预测RA码在混合信道上的性能。     

一特殊情形的三台可拒绝同型机在线排序问题

给定三台同型平行机，工件逐个到达，每个工件带有两个参数（tj，Pj），可以被接受加工，消耗一定的加工时间tj，也可以被拒绝，但要付出一定的罚值Pj，目标是要使被加工工件的最大完工时间makespan和拒绝工件的罚值之和最小．文中进一步假定每个工件的罚值和加工长度成固定的比例α∈[0，＋∞），针对工件加工不可中断情形，设计出近似算法PRL，证明其关于α的参数竞争比，进一步给出该问题的下界，它们均为α的分段函数．该算法在α∈[0，1/2）∪[1，＋∪）已达到最优．     

Balance sheets, exchange rate policy, and welfare

We evaluate the welfare implications of fixed and flexible exchange rate regimes in a small open-economy model that incorporates the financial accelerator coupled with liability dollarization. We solve the model up to a second-order approximation which allows us to rigorously address the relationship between uncertainty and welfare. We identify leverage and debt-to-GDP ratios above which an exchange rate peg is welfare superior to a flexible exchange rate regime. The results indicate that emerging market countries with even moderate levels of foreign currency-denominated debt may find it beneficial to stabilize their exchange rates.     

Analytical Value-at-Risk and Expected Shortfall under regime-switching

It is well known that the use of Gaussian models to assess financial risk leads to an underestimation of risk. The reason is because these models are unable to capture some important facts such as heavy tails and volatility clustering which indicate the presence of large fluctuations in returns. An alternative way is to use regime-switching models, the latter are able to capture the previous facts. Using regime-switching model, we propose an analytical approximation for multi-horizon conditional Value-at-Risk and a closed-form solution for conditional Expected Shortfall. By comparing the Value-at-Risks and Expected Shortfalls calculated analytically and using simulations, we find that the both approaches lead to almost the same result. Further, the analytical approach is less time and computer intensive compared to simulations, which are typically used in risk management.     

THE EXPECTED SHORTFALL OF QUADRATIC PORTFOLIOS WITH HEAVY‐TAILED RISK FACTORS

Computable expressions are derived for the Expected Shortfall of portfolios whose value is a quadratic function of a number of risk factors, as arise from a Delta–Gamma–Theta approximation. The risk factors are assumed to follow an elliptical multivariate t distribution, reflecting the heavy‐tailed nature of asset returns. Both an exact expression and a uniform asymptotic expansion are presented. The former involves only a single rapidly convergent integral. The latter is essentially explicit, and numerical experiments suggest that its error is negligible compared to that incurred by the Delta–Gamma–Theta approximation.