Linear Systems
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Normally, different financial institutions, i.e. banks, offer a variety of loans with different lending rates, according to a basic interest rate and the experience of the repayment patterns. In this paper, we construct and present a theoretic linear stochastic control model in order to evaluate the associated credit risk and obtain the optimal strategy for the determination of the level of the lending interest rates by optimizing the accumulated profit. Each sub-portfolio of loans is treated separately during a unit interval while at the end of the each time period there is some kind of solvency interaction. We assume that the repayment pattern follows a Brownian motion and using advanced optimization techniques, the optimal solutions are derived.