Research Overview 

My research focuses on principal-agent problems in financial mathematics, where one party (the agent) makes decisions on behalf of another (the principal) under uncertainty. A central question is how to design contracts that align the agent's actions with the principal's interests when the agent's strategy is not directly observable. 

Existing approaches to these problems rely on forward-backward stochastic differential equations - powerful but technically demanding machinery that limits broader applicability. Recent work has introduced PDE methods for settings where the agent controls only the drift of the output process. My dissertation extends this PDE framework to the more general case where the agent also controls volatility, which leads to fully nonlinear Hamilton-Jacobi-Bellman equations. 

This work bridges stochastic differential equations and partial differential equations, with applications in optimal investment, risk management, and the pricing of volatile commodities such as electricity.

Dissertation 

Principal-Agent Problems with Volatility Control 

Advisor: Professor John Chadam, University of Pittsburgh

Publications and Preprints 

Preprints 

C. Dissanayake. Partial Differential Equations Approach to Principal-Agent Problems with Volatility Control. (In preparation)

Publications

C.S.B. Dissanayake, U.D. Wijesooriya. On the construction of unitaries representing minimal inner toral polynomials. 

Journal of the National Science Foundation of Sri Lanka - November 2022 

Publications may also appear under Dissanayake, C.S.B.

Conference Presentations 

C.S.B. Dissanayake, U.D. Wijesooriya. A Method to Compute Unitaries Representing Reducible Minimal Inner Toral Polynomials using Direct Sum 

Ruhuna International Science and Technology Conference (RISTCON 2020)
Faculty of Science, University of Ruhuna, Matara, Sri Lanka - February 2021

C.S.B. Dissanayake, U.D. Wijesooriya. Behaviour of Pure Algebraic Isopairs at Non-Regular Points.

Postgraduate Institute of Science Research Congress (RESCON 2020)
Post Graduate Institute of Science, University of Peradeniya, Peradeniya, Sri Lanka - November 2020

Undergraduate Thesis 

Final Project - Thesis (B.Sc.)

Unitaries Representing Inner Toral Polynomials and Behaviour of Pure Algebraic Isopairs at Non-regular Points 

Final year project submitted to complete the Bachelor of Science (Special degree in Mathematics**)
at the University of Peradeniya.