4,076 research outputs found
Mean-field-game model for Botnet defense in Cyber-security
We initiate the analysis of the response of computer owners to various offers
of defence systems
against a cyber-hacker (for instance, a botnet attack), as a stochastic game
of a large number of interacting agents. We introduce a simple mean-field game
that models their behavior. It takes into account both the random process of
the propagation of the infection (controlled by the botner herder) and the
decision making process of customers. Its stationary version turns out to be
exactly solvable (but not at all trivial) under an additional natural
assumption that the execution time of the decisions of the customers (say,
switch on or out the defence system) is much faster that the infection rates
Optimal Cash Management Under Uncertainty
We solve an agent's optimization problem of meeting demands for cash over time with cash deposited in bank or invested in stock. The stock pays dividends and uncertain capital gains, and a commission is incurred in buying and selling of stock. We use a stochastic maximum principle to obtain explicitly the optimal transaction policy.Cash management, Stochastic control, Maximum principle, Risky assets
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