The First Stochastically Dominant Crypto-currency
Unlike all the other crypto-currencies that lack a proper monetary policy, our crypto-currency will provide a modern monetary policy that optimally adjusts to changes of output, inflation and other macro-economic variables.
Today, we are pleased to present the first stochastically dominant crypto-currency: for any investor, the best option would be to go long on the stochastically dominant crypto-currency instead of any of the previous crypto-currencies that didn’t implement an optimal monetary policy. In this way, you’ll own the optimal crypto-currency according to the best practices of modern macro-economics, in addition to being issued on our strictly-dominant blockchain.
And leaning on stochastic dominance, the following are some of the most market-impacting theorems:
- Theorem 10. A dominance relationship between the distribution of the monetary policy shock of the stochastically dominant crypto-currency over Bitcoin implies a rise of the price of the stochastically dominant crypto-currency in terms of Bitcoin (resp. any other PoW/PoS crypto-currency).
- Theorem 20. The efficient portfolio is to go long on the stochastically dominant crypto-currency: thus, the stochastically dominant strategy-proof allocation rule for any investor is to hold this efficient portfolio with the stochastically dominant crypto-currency. Furthermore, a higher return can be expected from the stochastically-dominant crypto-currency.
- Theorem 22. For any stochastic uncertainties ϵ ≥ 0 and η ≥ 0 , if the portfolio is approximately strategy-proof within ϵ and approximately efficient within η, then it induces an approximately efficient investment within ( ϵ + η ) ⋅ ( #Crypto-currencies ), independent of the other investors’ investments. Furthermore, the stochastically dominant crypto-currency induces a Nash equilibrium in the crypto-currency market that maximises ex ante social welfare.
- Theorem 26. Given a complete market M, two assets x and y will give to rise an arbitrage opportunity if and only: there exists a relationship of first-order stochastic dominance between the two assets; the price of the contingent claim between the two assets is non-positive.
An implementation is available at: https://github.com/Calctopia-OpenSource/cothority/tree/zkmonpolicy