Questions tagged [mathematics]
Used for question on application of mathematics in finance - from interest calculation to mathematical description of random processes.
195
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Understanding Price Elasticities in Discrete Choice Models (Derivative)
I'am in the midst of a paper on mutual fund product differentiation by Li and Qiu. Here, the authors model the utility an investor derives from investing in a mutual fund using a Discrete Choice Model ...
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2
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Why Ito calculus?
Coming from physics, I am used to the fact that the Ito interpretation of most natural stochastic equations is wrong, and one should be using Stratonovich calculus instead (of course they are ...
user8040
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Math basics of Equally-weighted Risk contributions
i'm writing my BA Thesis about "Equally-weighted Risk contributions". Can anyone recommend math books for further understanding of Risk contributions?
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2
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Is there a formula for future value of a growing annuity with yearly payment growth and monthly payments?
My example is saving for college:
assume a start of 0 balance
deposits of 200 made monthly, every year they increase by (g) 2% to account for salary increases, first deposit made at the end of the ...
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1
answer
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Distribution of minimum of hazard functions
Suppose I have two random variables, $X_1$ and $X_2$, that are independent (but not identically distributed) and assume both have hazard functions $\lambda_1(s)$ and $\lambda_2(s)$, for $s > 0$. ...
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Budget Constraint in Sharpe Ratio Optimization
I am a math student and I am trying to understand the budget constraint in Sharpe Ratio optimization for portfolio design. Recall the budget constraint requires that the sum of the portfolio weights ...
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1
answer
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Integration in the context of modelling with the Meixner Process
I failed to evaluate the integral of $\frac{e^{ax}}{x\sinh(bx)}$ with respect to $x$ from negative infinite to positive infinite. What techniques can I use to evaluate the integrals of such kind for ...
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PDE pricing of barrier options in BS
Path-dependent options in BS framework is intuitive to price with monte-carlo under risk-neutral measure, however it appears that several kinds can be priced with PDEs. I understand how does the story ...
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backward Kolmogorov equations - Markov properties
I'm a physicist who's research has lead him into the theory of stochastic differential equations. If this question is not appropriate for this forum, please feel free to delete it.
So I've been ...
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Why is that a risk averse consumer buys the optimum insurance when there is actuarially fair insurance?
I think I understand the fact that when marginal utilities of the same function are equal (a consequence of the actuarially fair insurance), the independent variables in it must be equal -- right? But ...
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Sampling and/or asymptotic distribution of a function
Assume we have the following function:
$$f(p) = \frac{1}{(1-p)d}\ln\left(\frac{1}{T}\sum_{t=1}^{T}\left[\frac{1+X_t}{1+Y_t} \right]^{1-p} \right)$$
where
$d$ is a constant
$T$ is a constant
$X_t$ ...
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How to rightfully balance the share of the organization between departments after variable changes?
This is an abstracted version of the problem I'm facing and I have to tell you first, my question might not be precise and or even correct, so I hope you understand and in that case can improve the ...
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Is it possible to understand financial theory without mathematics?
I am trying to develop a short course on financial theory, covering the fundamentals of forward and options pricing, and 'efficient market' theory. I want to reduce the amount of mathematics to a ...
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0
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FTAP in the model independent case, paper by Schachermayer
I have a question about the following paper by Beatrice Acciaio, Mathias Beiglböck, Friedrich Penkner, Walter Schachermayer. At the very beginning of the paper, on page 3, there are two definitions ...
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What is the right group of durations?
It seems that the group of durations commonly used in quantitative
analyse is $\mathbf{R}$ but it seems to me that $\mathbf{R_+^*}$ could
also be an interesting choice.
While I am not aware of ...
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1
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Get discount factors with limited knowledge?
I am facing the problem of just having this information:
6% coupon bond with 2.5 years to maturity, traded at a 100% clean price
4% coupon bond with 1.5 years to maturity, traded at a 98% clean price
...
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1
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Why is the discount function non increasing if pure cash holdings are feasible?
I am struggeling with the question, for example lets take a swap with rate of 3.2 for one year and 3.6 for 2 years and Discount Factor 0.96899 for the first year and 0.93158 for the second year.
...
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Proving the asymptotic distribution of Manipulation-Proof Performance Measure (MPPM) (Paper by Goetzmann et al.)
In Goetzmann et al.'s (2007) paper, the authors derive a "Manipulation-Proof Performance Measure" (MPPM), which is a performance measure that is impervious to performance manipulation by fund managers....
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Determine state price vectors?
I have 3 states with two assets, stocks and bonds.
The bond has a payoff of 1 in every state of the world.
And the stock has a current price of $S_0 = 100$ and ...
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0
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Does it make sense to apply complicated mathematics to calculate with precision when the margin of error is +/-10%? [closed]
This is more of a philosophical question than general question. Quantitative finance applies highly complicated mathematics and has attracted very smart people to this field lately given the high pay ...
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How to show that the risk contribution function is or is not injective?
Assume a portoflio $w \in \mathbb{R}^n$, you can get the total risk contribution $\psi_i$ of asset $i$ by doing:
$$\psi_i = w_i \frac{\partial \sigma(w)}{\partial w_i}= \frac{1}{\sigma(w)} \left[ w_i^...
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What is exactly Euler's decomposition?
I have often seen the following statement in different paper:
As $\sigma$ is homogeneous and of degree 1, we use Euler decomposition and write $\sigma(x)=\sum_{i=1}^n x_i \frac{\partial \sigma(x)}{\...
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What is the analytic value of an asset's risk contribution, if $n=2$?
The marginal risk contribution of asset $i$ is defined by Roncalli in his paper on ERC as follows:
$$\frac{\partial \sigma(x)}{\partial x_i} = \frac{1}{\sigma(x)} \left( w_i \sigma_i^2 + \sum_{\...
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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
And ...
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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 ...
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2
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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 $- ...
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4
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What are the options for a mathematician to break into QF without working for a fund? [closed]
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 ...
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0
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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 ...
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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 ...
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Proxy for a trigonometric angle function [closed]
You can't calculate an actual/real angle with the sine function with discrete market data.
I need a substitute value for inputs that require an angle value.
If you're only calculating the angle ...
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2
answers
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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 ...
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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 ...
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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 ...
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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?
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3
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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 ...
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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 ...
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votes
1
answer
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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 ...
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0
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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 ...
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1
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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 ...
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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?
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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 ...
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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
...
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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 ...
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What is a martingale?
What is a martingale and how it compares with a random walk in the context of the Efficient Market Hypothesis?
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15
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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 ...
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