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Research Proposal: PhD Application

Hello folks,

I'm applying for doctorate degrees in OR and Applied Mathematics (mostly in the US), and I have been suggested that I prepare a research proposal as some supervisors want it.

I am currently learning and navigating through concepts, and it is a little difficult to absorb so much information while doing my undergrad, in addition to reading enough literature to come up with a research proposal. However, my areas of interest so far are:
1. Advanced methods for pricing and hedging of derivative securities:
Subdomains: which include model jump with stochastic volatility; asymptotic methods in option pricing

2. Systemic risk:
Subdomain: quantitative models of financial stability

3. Stochastic control

Would really appreciate any tips on deciding on a research idea among these areas, and any further tips regarding drafting a research proposal would be appreciated too!

Cheers,
Aspiring quant
 
Read the abstracts of some recent papers in relevant journals to see what current (publishable) topics of interest are, then dig a bit deeper into the ones you find interesting. Often papers include some comments on directions of future research as well.
 
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