We consider option hedging and pricing for a large agent. The large agent affects the market’s demand-supply equilibrium and, therefore, the market prices of financial instruments. By assuming a specific large agent’s effect function for the underlying asset we derive the corresponding effect function for call options on that asset. As we show, the price of a call option in our model is the sol...

In  this  paper a  non-linear  model  with  fractional  order  is  presented  for  analyzing  and  controlling the  spread  of  HIV virus.  Both  the  disease-free  equilibrium and the endemic equilibrium are  found  and  their  stability is  discussed. The basic reproduction number , which is a function of the constant parameters in the model, plays an essential  role in the stability of  the ...

In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 < 1, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using compa...

A set of equilibrium states in a system consisting of economic agents, economic reservoirs, and firms is considered. Methods of irreversible microeconomics are used. We show that direct sale/purchase leads to an equilibrium state which depends upon the coefficients of supply/demand functions. To reach the unique equilibrium state it is necessary to add either monetary exchange or an intermediat...

This paper explores the merits of hedging stochastic input costs (i.e., reducing the risk of adverse changes in costs) in a decentralized, risk neutral supply chain. Specifically, we consider a generalized version of the well-known ‘selling-to-the-newsvendor’ model in which both the upstream and the downstream firms face stochastic input costs. The firms’ operations are intertwined – i.e., the ...