Numerical optimisation of time series / balance sheet

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Have an excel financial model, that pretty much is a time series of assets and liabilities. I would like to know what the optimal liability structure / mix is, subject to multiple balance sheet constraints. My objective function is to minimise funding cost.

I tried to optimise using Excel Data Solver, but encountered the following issues:

  • Excel may not arrive at a solution (can't converge at times even though there is a solution)
  • Solution is not consistent, eg same starting point (ie initial guess) but different end points (not all are optimum)
  • Solution may not be global minimum

Am open to using other softwares like Matlab or Mathematica, with my own "constraints"

  • I won't be able to simplify this down to an analytical equation so will need to be in the format of a financial time series model
  • Ideally arriving at global minimum
  • Scalable

Are there any guide you can point me to? Open to software suggestions, algorithms, approach, etc...

Thanks