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- Lahore University of Management Sciences
- LibGuides
- Numerical Solutions of Differential Equations
- LUMS; MATHEMATICS LABS

**FINANCIAL MATHEMATICS, STOCHASTIC PORTFOLIO**

Stochastic Portfolio Theory is a branch of Mathematical Finance. Robert Merton studied the portfolio allocation problem as a Stochastic Control Problem. In his model, an investor allocates his/her wealth between a risky asset and a riskless asset, then chooses the consumption rate to maximize the total expected utility

C* Algebras were first studied in connection with modeling observables in quantum mechanics. They have subsequently generated a lot of interest as an area of research. Fixed point theory is the investigation of existence, uniqueness, and approximation of fixed points of mappings. From economics (Nash’s theorem) to physics (phase transitions) there is a wide variety of applications of this exciting area of research. Dr. Shah’s research focuses on these two areas.

Modeling of complex biological phenomena has become fashionable over the past two decades, as the computing power required to analyze such models has become available. On the other side, non-local calculus has gained significance owing to its applications in various biological and physical phenomena. The theory of non-local calculus has to be developed to better analyze and understand these physical and biological phenomena