Deterministic and stochastic optimization in insurance

Luca Vincenzo Ballestra

  • Date:

    01 MAY
    20 JUNE 2024
     from 11:00 to 16:00
  • Event location: Aula IV, Department of Statistical Sciences, Via Belle Arti 41 (STAT PhD Classes Virtual Room on need)

  • Type: Cycle 39 - Short courses and seminars

Aims: The first part of the course is devoted to introducing the two main methodologies for dynamic optimization in continuous time, namely, the Pontryagin maximum principle and the Hamilton–Jacobi–Bellman (HJB) partial differential equation. The HJB approach will be taught in both the deterministic and stochastic settings. The second part of the course is devoted to practical applications of the theory and methods acquired in the first part. Specifically, the Merton portfolio optimization problem and the problem of choosing the optimal premium for an insurance policy will be considered.

Learning outcomes: After completing the course, students should have acquired the main techniques to solve deterministic and stochastic optimization problems in continuous time.

Final exam: Group presentation.

Course contents
- The Pontryagin maximum principle for deterministic dynamic optimization problems in continuous time
- The Hamilton–Jacobi–Bellman (HJB) partial differential equation for deterministic and stochastic dynamic optimization problems in continuous time
- Applications of the Pontryagin maximum principle and the HJB partial differential equation to problems in finance and insurance


Fleming, W. H., Rishel, R. W., Deterministic and Stochastic Optimal Control, Springer (1975)

Research papers
- Emms, P., Haberman, S., Pricing General Insurance Using Optimal Control Theory, AstinBulletin35, pp. 425-453 (2005)
- Emms, P., Dynamic Pricing of General Insurance in a Competitive Market, AstinBulletin37, 1-34 (2007)
- Gao, J., Optimal portfolios for DC pension plans under a CEV model, Insurance: Mathematics and Economics 44, 479–490 (2009)
- Merton, R. C. "Lifetime Portfolio Selection under Uncertainty: the Continuous-Time Case". The Review of Economics and Statistics, 51, 247–257 (1969)