OPTIMAL FINANCING AND DIVIDEND STRATEGIES IN A DUAL MODEL WITH PROPORTIONAL COSTS

We consider the optimal control problem with dividend payments
and issuance of equity in a dual risk model. Such a model might be appropriate
for a company that specializes in inventions and discoveries, which pays costs
continuously and has occasional profits. Assuming proportional transaction
costs, we aim at finding optimal strategy which maximizes the expected present
value of the dividends payout minus the discounted costs of issuing new equity
before bankruptcy. By adopting some of the techniques and methodologies in
Lφkka and Zervos (2008), we construct two categories of suboptimal models,
one is the ordinary dual model without issuance of equity, the other one assumes
that, by issuing new equity, the company never goes bankrupt. We identify
the value functions and the optimal strategies corresponding to the suboptimal
models in two different cases. For exponentially distributed jump sizes, closedform solutions are obtained.