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In many cases, clients want to be fully invested and don't want their assets lying around in cash. Hence the budget constraint $\sum_i w_i = 1$ is fairly common in practice. By the way, there are also cases where the constraint $\sum_i w_i = 0$ is applied: the result is a dollar neutral portfolio with long and short positions, but no net investment (short ...


I see your argument with the math. "1" is an arbitrary choice of positive numbers, and you could choose anything. In the end, you're going to scale the whole thing to fit your capital anyway. If you are using a numerical optimizer, it will be happier with something noticeably away from 0 and away from infinity, so I recommend choosing a specific positive ...


Portfolio management is about solving problems in the real world. In the real world, it is highly unlikely that EVERY asset has a negative expected return. If all the assets in your universe have negative returns, expand your universe to include a short-term fixed income security that is bound to produce a return greater than (or at a minimum equal to) ...


Some more concrete sources on Barrier option in the B&S setting and PDEs PDE methods for pricing barrier options (quite technical) Pricing Europ ean Barrier Options More of a general remark to PDE approaches in finance Ilya as far as I know the literature on that topic is quite limited. Solving a PDE means solving a PDE - it does not matter in ...


The initial condition for the backward Kolmogorov PDE is that $$ u(0,x) = g(x) $$ for all $x$ in the relevant domain and not just at a particular point. So if your functions $f$ and $g$ agree only at a single point the initial conditions are in fact different.


this is related to the concept of Jensen inequality. basically, $\frac{f(x-|\delta|)+f(x+|\delta|)}{2}\ne f(x)$, for convex functions it's $>f(x)$, and for concave ones $<f(x)$. risk averse guys have concave utilities, that's the relation you need to look at


Look at randommatrixportfolios.com

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