Work out Optimum Risk Hedging Frontier

From the last few days I was trying to find an optimum risk-hedging frontier (RHF) like what we had in our Economics graduation courses such as Production Possibility frontier. In the horizontal axis we suppose regions where the business are getting expanded and/or contracted and in the Y-axis we keep the business verticals. See the following image where I have tried to describe a basic architecture as to how all the 5 business verticals could be spread all across the continents and the question is, how efficient the frontiers would like be so that business could operate on a pre-defined frontier hedging the risk across vertically and horizontally both.

But the real problem is that, I could hardly draw a pentagon or hexagon so that in the point of intersection we could draw a business utility curve satisfying both the first and the second order conditions of profit maximization. Spend a lot of time but without concrete result. I need some guidance 😦 or productive discussion needed.

risk hedging frontier

risk hedging frontier

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