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I understand that it's possible, thankfully, to have your dissertation in a different topic from your master's thesis, but I seem to have a problem (see below). Do you know any other problems might I run into?

Background on me:

I am finishing up my master's in mathematical finance and now plan to pursue a PhD with my dissertation being in stochastic analysis/calculus, a branch of mathematics used in finance and physics.

My background on stochastic analysis:

I have had 3 classes related to stochastic analysis and 2 classes applying the concepts.

My thesis, being on the P-side of mathematical finance, has extremely little relevance to stochastic analysis, which is more used in the Q-side of mathematical finance.

The ONLY time stochastic analysis ever came up was encountering something in a paper that gives probabilities in the Q-side, and I thought of using a theorem to convert them to the P-side but later found out the paper was unnecessary or inapplicable (I forgot; I think I figured out another solution).

One problem I seem to have:

Some PhD applications seem to require a PhD proposal including a hypothesis, literature review and methodology.

I am not quite sure how mathematical research is conducted. Most of my research has been mainly in finance and statistics. What might I be able to do about this?

I am considering taking a second master's if needed but hopefully it need not come to that.

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BCLC
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    On a funny (?) note, in my university (or better, in my faculty at least) it is uncommon to have the same topic for a MSc thesis and a PhD thesis. That is my case, and I have actually seen people frowning upon this. To some, it looks like cheating because you have already months or years of experience prior to beginning your PhD. –  Mar 25 '15 at 15:32
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    What country are we talking about here? In Germany, this is very common and you only continue working on your master thesis’s topic, if your thesis resulted in questions worth investigating as a PhD project or if both theses are part of a larger project (and of course, only, if you actually want to). – Wrzlprmft Mar 25 '15 at 15:38
  • @dgraziotin That is extremely comforting. Thank you. – BCLC Mar 25 '15 at 15:50
  • @Wrzlprmft Well in general? Any info is appreciated. US, UK, any European country, etc. Like your info. Very much appreciated and very comforting. Thanks :) – BCLC Mar 25 '15 at 15:52
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    Among the about 25 first years we had, I can think of one case in which the phd topic was a continuation of undergrad/masters focus. This doesn't answer your question, but the case described strikes me more as a rule than an exception. This was the US, but not math which might make a difference. – gnometorule Mar 25 '15 at 16:13
  • @MrMeritology Thanks for pointing out that my last paragraph may be confusing but that's not what I meant. Will edit. – BCLC Mar 27 '15 at 17:12
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    @Jack OK. Thanks for clarifying your intention. – MrMeritology Mar 27 '15 at 17:17
  • @MrMeritology Edited. – BCLC Mar 27 '15 at 17:27
  • @dgraziotin Edited (see last part please). I'm very sorry for the confusion. In my case, I feel I am actually changing fields. Technically, mathematical finance and stochastic analysis fall under mathematics, but I think the methodologies are different at least in my case as my thesis involved the part of mathematical finance that has to do with statistics and not the part that has to do with stochastic analysis. – BCLC Mar 27 '15 at 17:30
  • Your situation seems very specific to UK universities and PhD application process. I'm not familiar enough to answer. – MrMeritology Mar 27 '15 at 19:17
  • @MrMeritology I think other places besides the UK do that. Never mind the specifics. My primary concern is the methodology. Essentially, I've been doing mostly finance in the master's thesis and have no idea how to do mathematical research besides using stackexchange to do my homework for me. Do you think this will be problematic? Even if it's not for the PhD proposal like if my application was just like the US, is the shift in methodology going to be a problem during my PhD? Or will it being proposed hinder me from getting in in the first place? – BCLC Mar 27 '15 at 19:21
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    @Jack While using StackExchange to answer specific questions is good, it shouldn't be used "to do your homework for you". You can answer your question about methodology by reading research papers, esp. survey articles in the major journals. There are also journal articles specifically on research methods. Go find them. Do you know Google Scholar? https://scholar.google.com/scholar?q=methodology+%22stochastic+calculus%22+%22stochastic+analysis%22&btnG=&hl=en&as_sdt=0%2C5 – MrMeritology Mar 27 '15 at 20:23
  • @MrMeritology I was exaggerating. I meant the only kinds of non-financial, non-statistical mathematical research we did was problem sets if those count. I consider those research because I asked on stackexchange. Anyway I sort of found the answer elsewhere but thanks for the link and the info :) http://academia.stackexchange.com/questions/42304/with-a-background-in-mathematical-finance-and-desire-to-apply-for-a-mathematics?noredirect=1#comment94292_42304 – BCLC Mar 27 '15 at 21:22

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If you are accepted into a PhD program, you should consider your dissertation topic to be independent of, and separate from your masters thesis topic. A PhD dissertation is fundamentally different from a Masters thesis. A PhD dissertation is expected to make a new contribution to research (however small), whereas a Masters thesis is a summary and application of existing research. PhD dissertations are a deeper dive into a topic or research questions, and an attempt to shed new light on the topic or questions.

You may have a Masters thesis that leads naturally into a deeper investigation as a PhD dissertation. Or not. You should focus your attention on the topics and questions that motivate your interest in a PhD. What are the core, unanswered questions? Which of these questions can you, with your skills and interests, address with some chance of success?

Leave behind the details of your Masters thesis. Focus on what you have learned in the process, and what new skills or capabilities you have. Now, with these insights, you should engage with surveys of research in your field -- those describing the unsolved problems or most critical questions. How does your experience, education, and interests lead you to engage with these unsolved problems or critical questions?

MrMeritology
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  • I feel so bad. You presented such a great answer to a situation that is not really mine. Sorry for the confusion. My primary concern is "Focus on what you have learned in the process". My thesis was in the P-side of mathematical finance dealing mainly with statistics. I would imagine there would be stochastic analysis if my thesis was more int the Q-side of mathematical finance. Hence, I feel I have little background in mathematical research particularly for the methodology part of the PhD proposal I have to submit for some applications. – BCLC Mar 27 '15 at 18:54
  • Right so my questions are 1 what might I be able to do regarding the methodology problem? 2 what other problems might I run into? – BCLC Mar 27 '15 at 18:56