Optimize a portfolio of [Cash, Stock A, European Put on A (K, T = 6 months)] over a 1-month horizon. The portfolio is constructed today and held unchanged for one month. I have a stochastic volatility model for A calibrated to historical data (physical measure P). Optimisation is straightforward a) without the option or b) option valued only as ITM ignoring the remaining time value. The problem - expected market price in 1 month (Q measure) of 6month option. I can get its expected value (P measure) but it's not the same as expected market price. The proper solution - calibrate another model mapping P -> Q and use it to price options. Are there other solutions, workarounds, heuristics ? My best idea - use the option value computed under P, possibly with a penalty on large option positions. Notes I'm trying to avoid the explicit P → Q mapping, because it seems very difficult to model reliably. Another problem - I'm interested in >x10 option moves (I'm using options - as put insurance or speculative explosive far otm calls). Such situations are rare and likely depend on unusual market regimes (panic) and extreme implied volatility. so there is little data and many parameters to estimate, making calibration difficult. I feel the resulting model would be fragile, with errors that are difficult to detect.