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2

In R, the simplest way to brute force through a predefined number of portfolio combinations would be to simply iterate over them: set.seed(42) returns <- matrix(rnorm(200),40,5) weights <- list(c(1,0,0,0,0), c(0,1,0,0,0), c(0,0,1,0,0), c(0,0,0,1,0), c(0,0,0,0,1)) conf <- 0.99 sapply(...


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You have many different options. Firstly, you know the characteristic function for the log stock price and, using inversion, you can recover the (inverse) distribution and density function and simulate from these using a uniform draw. That's the brute force approach. The variance gamma process is typically represented as a difference of gamma processes or a ...


2

A quantitative barrier to a local martingale being a true martingale is integrability. An example is as follows: $\int_0^t f(s) dB_s$ where $B_s$ is a Brownian motion and $f$ progressively measurable is a strict local martingale if $(E\int_0^t |f(s)|^2 ds)^{\alpha/2}=\infty$ for some $\alpha$ between $0$ and $1$. This is taken from Corollary 4 of `Strict ...


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