This thesis studies ways of modelling instabilities in quasi-efficient markets. We consider quasi-efficient markets where arbitrage is possible, but is relatively small and short lived. Under such a assumption we derive optimal arbitrage strategy of one agent and consider possible ways of funding optimal strategy under stop-loss constraint. Optimal strategy is used to build a multi-agent model which defines the arbitrage dynamics, i.e. its mean- reverting behaviour. The influence of agents on the asset prices is modelled by means of permanent price impact function. Multi-agent model is self-consistent as it creates mean-reverting term of the same type under which the optimal strategy for one agent was derived. As we show adding stop-loss constraint creates possibility for market instabilities.