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The answer probably depends on what your utility is nearest to being proportional to the logarithm of.
Most likely your utility (so far as you have one) looks like other_stuff + f(wealth) where wealth = g(annual_income, liquid_assets, other_assets) or something of the kind, where f and g are functions about which we don't know very much. It's probably OK to assume that g is just a linear combination of its inputs. So it seems like there are two things to do.
And then you can try plugging the result into the Kelly formula, seeing how over-risky it feels, and (if you are so inclined) correcting for excess risk aversion not already factored into f.