The mathematics tag has no wiki summary.
-1
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2answers
110 views
What's the first time-integral of price called?
In general I'm wondering about the names of time-derivatives of price.
E.g. in physics the first few time-derivatives of position are:
f(x) = displacement
f'(x) = velocity
f''(x) = acceleration
...
8
votes
1answer
236 views
reasonable asymptotic elasticity in utility maximization (paper by Kramkov / Schachermayer)
I'm working through this paper by Kramkov and Schachermayer. I have a question about the proof of Lemma 3.6.
$\mathbf{Question}$ Why is the inequality $(3.13)$ true, i.e.
$$\lim\sup_n ...
7
votes
1answer
86 views
Utility maximisation
We have a general setting, i.e. we are working with the time interval $[0,T]$ and a $\mathbb{R}^d$ valued semimartingale $S$, which is assumed to be RCLL. In utility maximisation the goal is to ...
2
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0answers
59 views
How to correctly construct a value- and equally weighted portfolio consisting of property-types?
A problem of which I couldn’t find the answer on the forum is about the construction of equally-weighted and value-weighted portfolio.
I want to compute the equally-weighted property-type portfolio ...
8
votes
1answer
190 views
Hedging duality
We consider a financial market over the time interval $[0,T]$ where a risky asset is a semimartingale $S$. By $\mathbb{P}$ we denote the set of all equivalent local martingale measures (ELMM). We ...
3
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1answer
123 views
Foward-start option pricing
Consider a probability filtred space $(\Omega, \mathcal F, \mathbb F, \mathbb P)$, where $\mathbb F = (\mathcal F_t)_{0\leq t\leq T}$ satisfing the habitual conditions and is generated by $1 d $- ...
5
votes
1answer
112 views
Risk neutral valuation independent of $Q$?
This question is bothering me now for a while. Suppose given is a random payoff $f\in L^0(\mathcal{F}_T)$ at time $T$, where $L^0(\mathcal{F}_T)$ denotes the space of all $\mathcal{F}_T$-measurable ...
6
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1answer
108 views
Different definition of NFLVR
I attend a course in mathematical finance. In the first chapter we discus the absence of arbitrage in full generality. For this purpose we define the following sets:
...
5
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2answers
357 views
Why does the future price dominate the forward price and why doesn't the long rate fall?
There are two questions left about the book Term Structure: A graduate Course by Damir Filipovic, which bother me. The first one is about the Theorem, that the long rate never falls (p. 108). Why is ...
5
votes
1answer
142 views
How to derive the formula of a European Libor call option in a Libor Market Model?
I am struggling with the following two mathematical statements. The first is from the book "Term-structure Models: A Graduate Course - Damir Filipović" Suppose we have a deterministic function ...
6
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4answers
457 views
What are the options for a mathematician to break into QF without working for a fund?
I have a degree in mathematics, and I've worked as a statistician and done some programming work. I'm very strong in my math/stats/programming background and have browsed some QF books, and I'm very ...
3
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0answers
182 views
Monty Hall Model
Given a fixed time period,say 3 days, the stock/market can go up,down or stay sideways. A hedge fund can long, short or use rangebound(options strategy) to bet for that 3 days closing level.
Hedge ...
-5
votes
1answer
277 views
Can a programmer be a quant trader without knowing all that math and models? [closed]
Is it a requirement to be a math person in order to work as a quant trader? Have you seen a non-math good developer successful in this career?
2
votes
0answers
101 views
Measure change in a bond option problem
This is not a homework or assignment exercise.
I'm trying to evaluate $\displaystyle \ \ I := E_\beta \big[\frac{1}{\beta(T_0)} K \mathbf{1}_{\{B(T_0,T_1) > K\}}\big]$, where $\beta$ is the ...
1
vote
1answer
410 views
Hurst Exponent Calculation
I am trying to calculate the Hurst Exponent using Excel. I am facing a problem where the exponent value sometime goes beyond 1. Can someone share a link / material so that it will help me to calculate ...
4
votes
2answers
231 views
What is Heston's equation?
This paper mentions the elliptic Heston operator:
$Av:= -\frac y2(v_{xx}+2\rho\sigma v_{xy} + \sigma^2v_{yy}) - (c_0 - q - \frac y2)v_x + \kappa(\theta -y)v_y + c_0v$.
Then boundary value problem ...
4
votes
2answers
480 views
Implications of the Riemann hypothesis in finance?
I was recently at a seminar by a top hedge fund manager at a top university for finance students, when one of the finance professors asked him what do you think are important areas of research for my ...
9
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1answer
207 views
Is a linear combination of GARCH processes also a GARCH process?
If two time series follow a GARCH process, and a third is a linear combination of them, is the third also GARCH process?
5
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2answers
597 views
How does one go from measure P to Q(risk-neutral) when modeling an asset paying dividends?
I am really having a terrible time applying Girsanov's theorem to go from the real-world measure $P$ to the risk-neutral measure $Q$. I want to determine the payoff of a derivative based an asset ...
7
votes
1answer
220 views
When pricing options, what precision should I work with?
I'm wondering if there's any point at all in double-precision calculations, or whether it's ok to just do everything in single-precision, seeing how the difference on non-Tesla GPUs for single and ...
7
votes
1answer
458 views
application of lie groups in finance
Can some one kindly go over some of the applications and use of Lie groups in finance? The math is very rigorous and I don't fully understand it or the potential it could have.
Let me share some ...
2
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0answers
119 views
Optimal stop-loss reinsurance
What are some methods for optimizing stop-loss reinsurance? I've found an article on the minimization of the variance. I also know about the method of average-at-range.
Can we apply a method for ...
10
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1answer
397 views
Any recommendations for textbooks for an undergraduate course in mathematical finance? [closed]
I'll teach an introductory course on mathematical finance in the near future. The course is intended to entertain and broaden some well-prepared advanced undergrad mathematics majors, some physics ...
15
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5answers
2k views
Recommendations for books to understand the math in quantitative finance papers?
Can anyone recommend books that explain the math used in quantitative finance academic papers?
14
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6answers
1k views
How random are financial data series?
Pseudorandom number generators are often tested using e.g. a test suite like Diehard tests or Dieharder. If one would run these tests e.g. on stock market time series or other financial data, would ...
7
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1answer
270 views
Modified Durations of Different Noncallable Bonds and function of Maturity
I'm hoping someone could help me understand this subject better.
Basically I am reading a book and it shows a table
...
21
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4answers
2k views
Random matrix theory (RMT) in finance
The new kid on the block in finance seems to be random matrix theory. Although RMT as a theory is not so new (about 50 years) and was first used in quantum mechanics it being used in finance is a ...
9
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4answers
2k views
What is a martingale?
What is a martingale and how it compares with a random walk in the context of the Efficient Market Hypothesis?
32
votes
10answers
12k views
How can I go about applying machine learning algorithms to stock markets?
I am not very sure, if this question fits in here.
I have recently begun, reading and learning about machine learning. Can someone throw some light onto how to go about it or rather can anyone share ...
