This paper deals with the multivariate tail conditional expectation (MTCE) for generalized skew-elliptical distributions. We present tail conditional expectation for univariate generalized skew-elliptical distributions and MTCE for generalized skew-elliptical distributions. There are many special cases for generalized skew-elliptical distributions, such as generalized skew-normal, generalized skew Student-t, generalized skew-logistic and generalized skew-Laplace distributions.

In this paper, we develop a novel game theoretic model of the interactions between an EDoS attacker and the defender based on a signaling game that is a dynamic game of incomplete information. We then derive the best defense strategies for the network defender to respond to the EDoS attacks. That is, we compute the perfect Bayesian Nash Equilibrium (PBE) of the proposed game model such as the pooling PBE, separating PBE and mixed strategy PBE. In the pooling equilibrium, each type of the attacker takes the same action and the attacker's type is not revealed to the defender, whereas in the separating equilibrium, each type of the attacker uses different actions and hence the attacker's type is completely revealed to the defender. On the other hand, in the mixed strategy PBE, both the attacker and the defender randomize their strategies to optimize their payoffs. Numerical illustration is also presented to show the efficacy of the proposed model.

In this note, we consider dynamic assortment optimization with incomplete information under the capacitated multinomial logit choice model. Recently, it has been shown that the regret (the cumulative expected revenue loss caused by offering suboptimal assortments) that any decision policy endures is bounded from below by a constant times $\sqrt {NT}$, where $N$ denotes the number of products and $T$ denotes the time horizon. This result is shown under the assumption that the product revenues are constant, and thus leaves the question open whether a lower regret rate can be achieved for nonconstant revenue parameters. In this note, we show that this is not the case: we show that, for any vector of product revenues there is a positive constant such that the regret of any policy is bounded from below by this constant times $\sqrt {N T}$. Our result implies that policies that achieve ${{\mathcal {O}}}(\sqrt {NT})$ regret are asymptotically optimal for all product revenue parameters.

In this paper, we develop the lower–upper-bound approximation in the space of Laplace transforms for pricing American options. We construct tight lower and upper bounds for the price of a finite-maturity American option when the underlying stock is modeled by a large class of stochastic processes, e.g. a time-homogeneous diffusion process and a jump diffusion process. The novelty of the method is to first take the Laplace transform of the price of the corresponding “capped (barrier) option” with respect to the time to maturity, and then carry out optimization procedures in the Laplace space. Finally, we numerically invert the Laplace transforms to obtain the lower bound of the price of the American option and further utilize the early exercise premium representation in the Laplace space to obtain the upper bound. Numerical examples are conducted to compare the method with a variety of existing methods in the literature as benchmark to demonstrate the accuracy and efficiency.

This paper investigates the issue of stochastic comparison of multi-active redundancies at the component level versus the system level. Based on the assumption that all components are statistically dependent, in the case of complete matching and nonmatching spares, we present some interesting comparison results in the sense of the hazard rate, reversed hazard rate and likelihood ratio orders, respectively. And we also obtain two comparison results between relative agings of resulting systems at the component level and the system level. Several numerical examples are provided to illustrate the theoretical results.

This paper deals with pricing formulae for a European call option and an exchange option in the case where underlying asset price processes are represented by stochastic delay differential equations with jumps (hereafter “SDDEJ”). We introduce a new model in which Poisson jumps are added in stochastic delay differential equations to capture behaviors of an underlying asset process more precisely. We derive explicit pricing formulae for the European call option and the exchange option by proving a Lemma on the conditional expectation. Finally, we show that our “SDDEJ” model is meaningful through some numerical experiments and discussions.

In this paper, we discuss the problem of pricing discretely sampled variance swaps under a hybrid stochastic model. Our modeling framework is a combination with a double Heston stochastic volatility model and a Cox–Ingersoll–Ross stochastic interest rate process. Due to the application of the T-forward measure with the stochastic interest process, we can only obtain an efficient semi-closed form of pricing formula for variance swaps instead of a closed-form solution based on the derivation of characteristic functions. The practicality of this hybrid model is demonstrated by numerical simulations.