On a dividend problem with random funding.

Area of Science:

• Actuarial Science
• Financial Mathematics
• Risk Theory

Background:

• Ruin theory analyzes financial risk and solvency.
• Dividend maximization is crucial for insurer profitability.

Purpose of the Study:

• To modify the dividend maximization problem in ruin theory.
• To maximize the net present value of discounted dividends minus discounted funding costs.
• To incorporate proportional transaction costs and independent Poisson funding processes.

Main Methods:

• Utilizing a classical risk process framework.
• Modeling dividends using a common approach.
• Employing jump times of an independent Poisson process for funding decisions.
• Deriving an explicit solution for exponentially distributed claims.

Main Results:

• An explicit optimal strategy was determined for exponentially distributed claims.
• The optimal strategy's nature is significantly influenced by transaction cost size.
• Unfavorable surplus positions prior to ruin are identified for optimal refunding.

Conclusions:

• The derived optimal strategy provides a framework for managing insurer solvency and profitability.
• Refunding during adverse surplus situations is strategically recommended.
• Transaction costs play a pivotal role in shaping dividend and funding strategies.