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There's more than one way to do this. One common approach among indices is to take an iterative approach. For instance, you might identify the stocks with weights about 5%, then re-weight so that everything adds up to 1. Then you might identify the sectors that break the 10% limit and re-scale them to be less than 10%. Then re-scale everything to add up to ...


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To price financial instruments such as options, bonds and stocks must be priced so as to be "arbitrage free". The concept of arbitrage can be made precise by one of the fundamental ideas of quantitative finance, the so called Arbitrage Theorem. Put differently the Arbitrage Theorem provides a very elegant and general method for pricing derivative ...


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Optimization is definitely important in Quantitative Finance, especially for portfolio optimization where we maximize utility of the return of a portfolio as linear weighted vector of asset returns subject to a desired risk level: $$ \max_{w\in[0,1]^n} U(\mu_p(w),\sigma_p(w))\quad s.t. \sum_{i=1}^n w_i=1$$ where $w$ being the portfolio weights, and $U$ ...



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