Theology is the study of revelation and fundamental theology is the study of reasons to believe in revelation. The author gives a good account of the historical Jesus, but he is weak in fundamental theology.
Allison apparently thinks the historical Jesus only consists of what Jesus actually said and did. I don't agree at all. The historical Jesus also includes how his contemporaries perceived him. Jesus was not just a Jewish prophet who preached the coming of the kingdom of God. He was also an exorcist and healer, and his followers swore up and down that he appear to them after he died.
John Dominic Crossan and Marcus Borg, who do not believe in life after death, trace the Resurrection to within a few years of Jesus' crucifixion by Pontius Pilate (The First Christmas: What the Gospels Really Teach About Jesus's Birth). Crossan thinks that Jesus was buried in a mass grave, but Raymond Brown says it is historically certain that Jesus was buried in a separate tomb.
Denying that Jesus' followers had the Easter experience makes no sense because his followers founded the Catholic Church, and the Catholic Church gave us Western Civilization. When Christians lost their influence over governments, two centuries of war and genocide resulted.
This means that the Resurrection of Jesus is both an historical event and an object of faith. As an object of faith, the Resurrection means that Jesus is alive in a new life with God. Believing in Jesus means believing that if you follow Jesus the same good thing can happen to you.
Referring to the problem of evil, Allison says, "In fact, the memories about him [Jesus] offer, I suggest, some wisdom in the matter of what is perhaps the most intractable problem for Christian faith."
The problem of evil is the question: Why does God allow human beings to suffer so much? This is not one question but three. In the mind of an atheist, it is an argument against God's existence. In the mind of a nonbeliever, it is evidence that God does not care about our welfare. In the mind of a believer, it is a question about revelation.
The answer to the atheist is that evil does not exist because evil is the absence of being. The theological answer is that there is some higher good that God is achieving. We don't know what that higher good is, but it must be there.
The answer to the nonbeliever is that they are right. Human suffering is indeed evidence that God does not care about our welfare. One of the reasons to believe in God is that people who don't usually give bad reasons. They say God doesn't exist or that Jesus did not rise from the dead. They say free will is an illusion and humans are collections of molecules. When someone gives a good reason, it should be acknowledged. Faith is both a decision and a gift from God. We can summon people to believe Jesus is alive, but it is wrong to criticize their judgment if they don't believe.