Pr[|X −E[X]| ≥ a] = Pr[(x−E[x]) ≥ a] ≤ E[(x−E[x]) 2] a2 = Var[X] a2 1.3 Example: Coupon Collector Xi : # boxes bought when you have exactly i− 1 different coupons, and after buying these boxes, you have i different coupons. Let X = ∑ i∈nXi: # boxes one bought until at least one of every type of coupon is obtained. Let pi be the probability of obtaining a new coupon when we have exactly i−1 diff...

The paper analyzes the decision made by firms to issue one-time coupons as a means of attracting new deal-prone customers. Given the structure of the market and the share of loyal customers, we derive boundaries for the value of the coupon, as well as the optimal face value of the coupon. The main variables which determine the coupon value are: the size of deal-prone and loyal market segments, ...

Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier op...

In this paper we consider an approach to solve the minimum test collection problem. This approach is based on an explicit reduction from the problem to the satisfiability problem.

We present an explicit formula for European options on coupon bearing bonds and swaptions in the Heath-Jarrow-Morton (HJM) one factor model with non-stochastic volatility. The formula extends the Jamshidian formula for zero-coupon bonds. We provide also an explicit way to compute the hedging ratio (∆) to hedge the option with its underlying.

Collection of waste is an important logistic activity within any city. In this study, a mathematical model is proposed in order to reduce the cost of waste collection. First a mixed-integer nonlinear programming model is provided including a waste collection routing problem, so that, there is a balance between the distance between trashcans, and the similarity of the trashcans in terms of th...

Structural elements, such as stiffened panels, are designed by combining material strength data obtained from coupon tests with a failure theory for 3D stress field. Material variability is captured by dozens of coupon tests, but there remains epistemic uncertainty due to error in the failure theory, which can be reduced by element tests. Conservativeness to compensate for the uncertainty in fa...